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Abstract Background Crop phenotype extraction devices based on multiband narrowband spectral images can effectively detect the physiological and biochemical parameters of crops, which plays a positive role in guiding the development of precision agriculture. Although the narrowband spectral image canopy extraction method is a fundamental algorithm for the development of crop phenotype extraction devices, developing a highly real-time and embedded integrated narrowband spectral image canopy extraction method remains challenging owing to the small difference between the narrowband spectral image canopy and background. Methods This study identified and validated the skewed distribution of leaf color gradation in narrowband spectral images. By introducing kurtosis and skewness feature parameters, a canopy extraction method based on a superpixel skewed color gradation distribution was proposed for narrowband spectral images. In addition, different types of parameter combinations were input to construct two classifier models, and the contribution of the skewed distribution feature parameters to the proposed canopy extraction method was evaluated to confirm the effectiveness of introducing skewed leaf color skewed distribution features. Results Leaf color gradient skewness verification was conducted on 4200 superpixels of different sizes, and 4190 superpixels conformed to the skewness distribution. The intersection over union (IoU) between the soil background and canopy of the expanded leaf color skewed distribution feature parameters was 90.41%, whereas that of the traditional Otsu segmentation algorithm was 77.95%. The canopy extraction method used in this study performed significantly better than the traditional threshold segmentation method, using the same training set, Y1 (without skewed parameters) and Y2 (with skewed parameters) Bayesian classifier models were constructed. After evaluating the segmentation effect of introducing skewed parameters, the average classification accuracies Acc_Y1 of the Y1 model and Acc_Y2 of the Y2 model were 72.02% and 91.76%, respectively, under the same test conditions. This indicates that introducing leaf color gradient skewed parameters can significantly improve the accuracy of Bayesian classifiers for narrowband spectral images of the canopy and soil background. Conclusions The introduction of kurtosis and skewness as leaf color skewness feature parameters can expand the expression of leaf color information in narrowband spectral images. The narrowband spectral image canopy extraction method based on superpixel color skewness distribution features can effectively segment the canopy and soil background in narrowband spectral images, thereby providing a new solution for crop canopy phenotype feature extraction.

Item nonresponse is a common issue in surveys. Because unadjusted estimators may be biased in the presence of nonresponse, it is common practice to impute the missing values with the objective of reducing the nonresponse bias as much as possible. However, commonly used imputation procedures may lead to unstable estimators of population totals/means when influential units are present in the set of respondents. In this article, we consider the class of multiply robust imputation procedures that provide some protection against the failure of underlying model assumptions. We develop an efficient version of multiply robust estimators based on the concept of conditional bias, a measure of influence. We present the results of a simulation study to show the benefits of our proposed method in terms of bias and efficiency. [ABSTRACT FROM AUTHOR]

This article presents the problem of interval estimation of the mean, difference and ratio of means for zero-adjusted inverse Gaussian distributions. Confidence intervals of the mean are derived using signed log-likelihood, method of variance estimate recovery (MOVER), generalized variable, and Bayesian approaches. For two populations, we derive MOVER, generalized variable-based interval, and Bayesian intervals for the difference and ratio of means. We perform intensive simulations to compare the proposed confidence intervals of the function of parameters. Finally, illustrative examples are given using real data sets from different fields. [ABSTRACT FROM AUTHOR]

This study presents a novel distribution derived from the exponential distribution, referred to as the neutrosophic size-biased exponential distribution (NSBED). Various characteristics of the proposed model, including moments, skewness, and kurtosis, are investigated. Plots depicting the cumulative distribution function, density function, and other relevant functions associated with the survival analysis hazard function under indeterminacy are provided. Parameter estimates for the proposed model within the neutrosophic framework are computed. To illustrate the statistical applications of the results in handling imprecise data, a motivation is provided. A simulation analysis is conducted to validate the theoretical aspects of the proposed NSBED. Results indicate that the new distribution exhibits right skewness and shares many properties with skewed distributions. Our novel distribution outperforms the size-biased exponential distribution. Finally, a real application of the proposed model is provided to illustrate the practical implications. [ABSTRACT FROM AUTHOR]

Logistic regression models are commonly used to explain binary health outcome variable using independent variables such as patient characteristics in medical science and public health research. Although there is no distributional assumption required for independent variables in logistic regression, variables with severely right-skewed distribution such as lab values are often log-transformed to achieve symmetry or approximate normality. However, lab values often have zeros due to limit of detection which makes it impossible to apply log-transformation. Therefore, preprocessing to handle zeros in the observation before log-transformation is necessary. In this study, five methods that remove zeros (shift by 1, shift by half of the smallest nonzero, shift by square root of the smallest nonzero, replace zeros with half of the smallest nonzero, replace zeros with the square root of the smallest nonzero) are investigated in logistic regression setting. To evaluate performances of these methods, we performed a simulation study based on randomly generated data from log-normal distribution and logistic regression model. Shift by 1 method has the worst performance, and overall shift by half of the smallest nonzero method, replace zeros with half of the smallest nonzero method, and replace zeros with the square root of the smallest nonzero method showed comparable and stable performances. [ABSTRACT FROM AUTHOR]

We investigate the statistical mechanism of clicks and replies to posts on the BBS forum. Empirical analysis indicates that the heavy-tailed distribution of replies is correlated and determined by similarly skewed distribution of clicks. The investigation suggests that the highly skewed distribution of one could result from the skewed distribution of the other. Power law distribution of both replies and clicks can be interpreted as the macro behaviours of the systems that consist of micro units. The empirical results of this paper provide another perspective for us to understand collective online behaviour.

Only a few scientists are able to publish a substantial number of papers every year; most of the scientists have an output of only a few publications or no publications at all. Several theories (e.g., the "sacred spark" theory) have been proposed in the past to explain these productivity differences that are complementary and focus on different aspects in the publication process. This study is intended to introduce a research program for studying productivity differences in science (skewed distributions of scientists' productivity). The program is based on the Anna Karenina Principle (AKP). The AKP states that success in research is the result of several prerequisites that are multiplicatively related. Great success results from prerequisites that must be all given. If at least one prerequisite is not given, failure follows, whereby the failure is specific to the set of given and missing prerequisites. High productivity is given for the few scientists who fulfill all prerequisites (e.g., high motivation, pronounced creativity, reputational professional position, early important papers in high-impact journals), and low productivity is connected to a specific combination of missing and fulfilled prerequisites for many scientists. Besides the AKP as theoretical principle, the program for studying productivity differences includes a mathematical concept explaining skewed distributions and statistical methods for empirical productivity analyses. [ABSTRACT FROM AUTHOR]

In this study, a new three-parameter distribution is introduced by extending the two-parameter Alpha Power Inverse Rayleigh distribution using Marshall-Olkin G approach. The proposed Marshall-Olkin Generalized Alpha Power Inverse Rayleigh (MOAPIR) distribution generalizes the Marshall-Olkin Inverse Rayleigh, Alpha Power Inverse Rayleigh, and Inverse Rayleigh distribution. The characterization and statistical properties of the proposed distribution such as hazard rate function, reversed hazard rate function, quantiles, moments, and order statistics were derived. The estimation of the MOAPIR distribution parameters is derived using the maximum likelihood estimation method. The performance of the proposed distribution was compared with other competing distribution using two real-life data. The goodness of fit criteria and the distribution function curve showed that the proposed distribution provides a better fit than other competing distributions of the same family of heavily positive skewed distribution. [ABSTRACT FROM AUTHOR]

In many statistical analysis, a finite population may contain a large proportion of zero-and-one values that make the population distribution severely skew. Confidence intervals based on a normal approximation (NA) for such data may have low coverage probabilities. In this paper, we apply the methods of jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) to discuss the confidence intervals for the mean of zero-and-one inflated population. Asymptotic distributions of the likelihood-type statistics are studied. Simulations are conducted to compare coverage probabilities with other methods under different distributions. Real data is given to illustrate the procedure of proposed methods. [ABSTRACT FROM AUTHOR]

Developing a confidence interval for the ratio of two quantities is an important task in statistics because of its omnipresence in real world applications. For such a problem, the MOVER-R (method of variance recovery for the ratio) technique, which is based on the recovery of variance estimates from confidence limits of the numerator and the denominator separately, was proposed as a useful and efficient approach. However, this method implicitly assumes that the confidence interval for the denominator never includes zero, which might be violated in practice. In this article, we first use a new framework to derive the MOVER-R confidence interval, which does not require the above assumption and covers the whole parameter space. We find that MOVER-R can produce an unbounded confidence interval, just like the well-known Fieller method. To overcome this issue, we further propose the penalized MOVER-R. We prove that the new method differs from MOVER-R only at the second order. It, however, always gives a bounded and analytic confidence interval. Through simulation studies and a real data application, we show that the penalized MOVER-R generally provides a better confidence interval than MOVER-R in terms of controlling the coverage probability and the median width. [ABSTRACT FROM AUTHOR]

This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull, exponential, Pareto, and log-logistic baseline distributions. The study establishes metrics for local dependency and examines the significant characteristics of the proposed bivariate model. To provide greater flexibility, a multivariate version of the continuous FGMLG family are suggested. Bayesian and maximum likelihood methods are employed to estimate the model parameters, and a Monte Carlo simulation evaluates the performance of the proposed bivariate family. Finally, the practical application of the proposed bivariate family is demonstrated through the analysis of four data sets.

This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull, exponential, Pareto, and log-logistic baseline distributions. The study establishes metrics for local dependency and examines the significant characteristics of the proposed bivariate model. To provide greater flexibility, a multivariate version of the continuous FGMLG family are suggested. Bayesian and maximum likelihood methods are employed to estimate the model parameters, and a Monte Carlo simulation evaluates the performance of the proposed bivariate family. Finally, the practical application of the proposed bivariate family is demonstrated through the analysis of four data sets. [ABSTRACT FROM AUTHOR]

Gravity-aided navigation is an effective navigation method for underwater vehicles. However, the distribution of the gravity field may affect the measurement errors of gravity anomalies and the precision of gravity-aided navigation. In this paper, the upper and lower thresholds of the gravity field standard deviation are computed by the statistical properties of the local gravity field to classify each grid in the gravity map into different levels. A parallel multiple methods with adaptive decision making (PMMADM) for gravity-aided navigation is proposed which incorporates the gravity anomaly measurements, particle filtering, and maximum correlation method into the observation equation of the extended Kalman filter. The algorithm autonomously selects the observation variables in the filter by combining the gravity field standard deviation at the current position of the carrier with a decision tree. This approach can combine the characteristics of different gravity matching algorithms, reduce the impact of random noise in the measurements, and improve the positioning accuracy of gravity-aided navigation. Physical simulation experiments demonstrated that the proposed gravity matching algorithm achieves the high navigation accuracy and long-term stability in different gravity fields, and the mean value of positioning error is 620.72 m. [ABSTRACT FROM AUTHOR]

The bias correction method (BCM) is useful in reducing the statistically downscaled biases of global climate models’ (GCM) outputs and preserving statistical moments of the hydrological series. However, BCM is less efficient under changed future conditions due to the stationary assumption and performs poorly in removing bias at extremes, thereby producing unreliable bias-corrected data. Thus, the existing BCM with normal distribution is improved by incorporating skewed distributions into the model with linear covariate (BCM-QMskewed). In this study, BCM-QMskewed is developed to reduce biases in the extreme temperature data of peninsular Malaysia. The input is the MIROC5 model output gridded data and observations sourced by the Malaysian Department of Irrigation and Drainage (1976–2005). BCM-QMskewed with lognormal (LGNORM) and Gumbel (GUM) has shown considerable skill in correcting biases, capturing extreme and nonstationarity of current and future extreme temperatures data series corresponding to the representative concentration pathways (RCPs) for 2006–2100 based on model diagnostics and precision analysis. Higher projection of extreme temperatures is more pronounced under RCP8.5 than RCP4.5 with precise estimates ranging from 33 to 42 °C and 30 to 32 °C, respectively. Finally, the projection of extreme temperatures is used to calculate cardiovascular disease (CVD) mortality rate which coincides with high extreme temperatures ranging between 0.002 and 0.014. HIGHLIGHTS BCM-QMskewed with LGNORM and GUM was considered to capture the extreme values.; The linear covariate model was considered to capture the nonstationary trend in extreme temperatures series.; Results indicate the model's ability to correct the biases of extreme temperatures data for both RCPs in the study area with decent accuracy.; Higher mortality rate of CVD is consistent with higher extreme temperatures.;

Gravity-aided navigation is an effective navigation method for underwater vehicles. However, the distribution of the gravity field may affect the measurement errors of gravity anomalies and the precision of gravity-aided navigation. In this paper, the upper and lower thresholds of the gravity field standard deviation are computed by the statistical properties of the local gravity field to classify each grid in the gravity map into different levels. A parallel multiple methods with adaptive decision making (PMMADM) for gravity-aided navigation is proposed which incorporates the gravity anomaly measurements, particle filtering, and maximum correlation method into the observation equation of the extended Kalman filter. The algorithm autonomously selects the observation variables in the filter by combining the gravity field standard deviation at the current position of the carrier with a decision tree. This approach can combine the characteristics of different gravity matching algorithms, reduce the impact of random noise in the measurements, and improve the positioning accuracy of gravity-aided navigation. Physical simulation experiments demonstrated that the proposed gravity matching algorithm achieves the high navigation accuracy and long-term stability in different gravity fields, and the mean value of positioning error is 620.72 m.

This paper adopts a bootstrap procedure in the maximum pseudo-likelihood method under probability sampling designs. It estimates the mean of a population that is a mixture of excess zero and a nonzero skewed sub-population. Simulations studies show that the bootstrap confidence intervals for zero-inflated log-normal population consistently capture the true mean. The proposed method is applied to a real-life data set. [ABSTRACT FROM AUTHOR]

Identifying key factors from observational data is important for understanding complex phenomena in many disciplines, including biomedical sciences and biology. However, there are still some limitations in practical applications, such as severely nonlinear input–output relationships and highly skewed output distributions. To acquire more reliable sensitivity analysis (SA) results in these extreme cases, inspired by the weighted k-nearest neighbors algorithm, we propose a new method called adaptive weighted neighbors (AWN). AWN makes full use of the information contained in all training samples instead of limited samples and automatically gives more weight to nearby samples. Then, the bootstrap technique and Jansen's method are used to obtain reliable SA results based on AWN. We demonstrate the performance and accuracy of AWN by analyzing various biological and biomedical data sets, three simulated examples and two case studies, showing that it can effectively overcome the above limitations. We therefore expect it to be a complementary approach for SA. [ABSTRACT FROM AUTHOR]

The skewed class distribution and data complexity may severely affect the imbalanced classification results. The cost of classification can be significantly reduced if these data complexity are measured and pre-processed prior to training, particularly when dealing with large-scale and high-dimensional datasets. Although many methods have been proposed to evaluate data complexity, most of them fail to fully consider the interaction among different data characteristics, or the connection between class imbalance and these characteristics, thus posing a serious challenge to effectively evaluate the difficulty of classification. This paper presents a new data complexity measure MFII (multi-factor imbalance index), which measures the combined effects of the skewed class distribution and data characteristics on classification difficulty. In particular, it further comprehensively investigates the impact of overlap size, confusion degree, and sub-cluster structure. VoR (value of resolution) and DoC (degree of consistency) are also proposed to evaluate the resolution and interpretability of complexity measures. The experimental results demonstrate that MFII has lower VoR and a stronger correlation with classification metrics, which indicates that MFII can more accurately evaluate the difficulty of multi-class imbalanced classification tasks. • MFII considers class imbalance and various overlap factors to assess data complexity. • VoR and DoC are proposed to estimate resolution and stability of complexity measures. • MFII has strong negative correlation with classification results. [ABSTRACT FROM AUTHOR]

Point cloud registration methods based on Gaussian Mixture Models (GMMs) exhibit high robustness. However, GMM cannot precisely depict point clouds, because the Gaussian distribution is spatially symmetric and local surfaces of point clouds are typically non-symmetric. In this paper, we propose a novel method for rigid point cloud registration, termed coherent point drift with Skewed Distribution (Skewed CPD). Our method employs an asymmetric distribution constructed from the local surface normals and curvature radii. Compared to the Gaussian distribution, this skewed distribution provides a more accurate spatial description of points on local surfaces. Additionally, we integrate an adaptive multiplier to the covariance, which reallocates the weight of the covariance for different components in the probabilistic mixture model. We employ the EM algorithm to address this maximum likelihood estimation (MLE) issue and leverage GPU acceleration. In the M-step, we adopt an unconstrained optimization technique rooted in a Lie group and Lie algebra to attain the optimal transformation. Experimental results indicate that our method outperforms state-of-the-art methods in both accuracy and robustness. Remarkably, even without loop closure detection, the cumulative error of our approach remains minimal. • Substitute Gaussian distribution with skewed distribution for enhanced accuracy in probability models. • Construct the probability density function using local surface normals and curvature radii. • Apply an adaptive multiplier to each probability component's covariance. • Utilize Lie-group-based unconstrained optimization for the M-step in the EM algorithm. • Without loop closure detection, outperform other advanced registration methods in cumulative error. [ABSTRACT FROM AUTHOR]

The high quality and efficient production of greenhouse vegetation depend on micrometeorology environmental adjusting such as system warming and illumination supplement. In order to improve the quantity, quality, and efficiency of greenhouse vegetation, it is necessary to figure out the relationship between the crop growth conditions and environmental meteorological factors, which could give constructive suggestions for precise control of the greenhouse environment and reduce the running costs. The parameters from the color information of the plant canopy reflect the internal physiological conditions, thus, the RGB model has been widely used in the color analysis of digital pictures of leaves. We take photographs of Begonia Fimbristipula Hance (BFH) growing in the greenhouse at a fixed time every day and measure the meteorological factors. The results showed that the color scale for the single leaf, single plant, and the populated canopy of the BFH photographs all have skewed cumulative distribution histograms. The color gradation skewness-distribution (CGSD) parameters of the RGB model were increased from 4 to 20 after the skewness analysis, which greatly expanded the canopy leaf color information and could simultaneously describe the depth and distribution characteristics of the canopy color. The 20 CGSD parameters were sensitive to the micrometeorology factors, especially to the radiation and temperature accumulation. The multiple regression models of mean, median, mode, and kurtosis parameters to microclimate factors were established, and the spatial models of skewness parameters were optimized. The models can well explain the response of canopy color to microclimate factors and can be used to monitor the variation of plant canopy color under different micrometeorology. [ABSTRACT FROM AUTHOR]

Several assumptions such as normality, linear relationship, and homoscedasticity are frequently required in parametric statistical analysis methods. Data collected from the clinical situation or experiments often violate these assumptions. Variable transformation provides an opportunity to make data available for parametric statistical analysis without statistical errors. The purpose of variable transformation to enable parametric statistical analysis and its final goal is a perfect interpretation of the result with transformed variables. Variable transformation usually changes the original characteristics and nature of units of variables. Back-transformation is crucial for the interpretation of the estimated results. This article introduces general concepts about variable transformation, mainly focused on logarithmic transformation. Back-transformation and other important considerations are also described herein.

Abstract Background Image processing techniques have been widely used in the analysis of leaf characteristics. Earlier techniques for processing digital RGB color images of plant leaves had several drawbacks, such as inadequate de-noising, and adopting normal-probability statistical estimation models which have few parameters and limited applicability. Results We confirmed the skewness distribution characteristics of the red, green, blue and grayscale channels of the images of tobacco leaves. Twenty skewed-distribution parameters were computed including the mean, median, mode, skewness, and kurtosis. We used the mean parameter to establish a stepwise regression model that is similar to earlier models. Other models based on the median and the skewness parameters led to accurate RGB-based description and prediction, as well as better fitting of the SPAD value. More parameters improved the accuracy of RGB model description and prediction, and extended its application range. Indeed, the skewed-distribution parameters can describe changes of the leaf color depth and homogeneity. Conclusions The color histogram of the blade images follows a skewed distribution, whose parameters greatly enrich the RGB model and can describe changes in leaf color depth and homogeneity.

In this paper, we develop a new general class of skew distributions with flexibility properties on the tails. Moreover, such class can provide heavy and light tails. Some of its mathematical properties are studied, including the quantile function, the moments, the moment generating function and the mean of deviations. New skew distributions are derived and used to construct new models capturing asymmetry inherent to data. The estimation of the class parameters is investigated by the method of maximum likelihood and the performance of the estimators is assessed by a simulation study. Applications of the proposed distribution are explored for two climate data sets. The first data set concerns the annual heat wave index and the second data set involves temperature and precipitation measures from the meteorological station located at Schiphol, Netherlands. Data fitting results show that our models perform better than the competitors. [ABSTRACT FROM AUTHOR]

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The non-normality may occur in the data due to several reasons such as the presence of the outlier or skewness. It leads to lose the power and fail control Type I error probability of the tests which are used to test the equality of the group means under heteroscedasticity. To overcome this problem, a revised generalized F-test (RGF) is proposed to test the equality of group means under heteroscedasticity in which non-normality is caused by skewness in this study. An extensive Monte-Carlo simulation study is conducted to investigate and compare the performance of the proposed test with non-parametric alternatives under several values of skewness, and different number of groups. The proposed RGF is the best choice in the high level of skewness for k = 3, 4, 5. The Kruskal-Wallis test shows better performance than the others in small and moderate sample sizes for k = 6, and 7. It is shown that the proposed RGF test is superior than the non-parametric alternatives in the most of the conditions. [ABSTRACT FROM AUTHOR]

The robust control network for nonlinear large-scale systems with parametric uncertainties also considers the uncertain robust stabilization problem for controlled networks. In heterogeneous populations, hybrid regression models are the most important statistical analysis tools. To aim of the study is to conduct a more in-depth analysis of the existing completive robust control networks relying on biased temporal logic. Compared with the symmetric distribution, the skewed distribution can obtain accurate and effective information. Therefore, a time-series logic model under skewed distribution is proposed. The temporal logic under skew state is applied to describe the normative language of fuzzy systems. Firstly, the mixed nonlinear regression model under skewed distribution data is introduced to test whether the temporal logic formula can be realized under the skew state. Secondly, through the method of reduction, the control flow interval logic CFITL is studied, and the time series logic sequence is used to describe the measurement output loss. The sufficient conditions for the control network system to satisfy the exponential stability and H ∞ performance index are given. The linear matrix inequality obtains the completeness control network to be designed, and the effectiveness of the proposed method is verified by stochastic simulation experiments. Finally, the method is verified to be practical and feasible based on actual data. The maximum recognition rates of nearest neighbor classification, nearest subspace classification and biased distribution temporal logic classification reached 0.9019, 0.9622 and 0.9304, respectively. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new general family of skewed distributions obtained through the use of a weighted skewed technique. This technique has the feature to unify two classical skewness techniques. Also, it is based on a clear stochastic representation involving a tuning weight function. General moments results are given. Subsequently, we focus our attention on a special case called asymmetric bimodal normal distribution. We investigate the maximum likelihood estimation of the parameters for this new distribution, with a complete numerical study. The developed model and method of inference are applied to some daily closing prices of some popular stocks. [ABSTRACT FROM AUTHOR]

Many variables encountered in practice have skewed distributions. While the sample mean is unbiased for the true mean regardless of the underlying distribution that generated the sample observations, it can be highly unstable in the context of skewed distributions. To cope with this problem, we propose an efficient estimator of the population mean based on the concept of conditional bias of a unit, which can be viewed as a measure of its influence. The idea is to reduce the impact of the sample units that have a large influence. The resulting estimator depends on a cut‐off value. We suggest selecting the cut‐off value that minimizes the maximum absolute estimated conditional bias with respect to the proposed estimator. An estimator of the mean square error is also presented. An empirical investigation comparing several estimators in terms of relative bias and relative efficiency suggests that the proposed estimator and the estimator of its mean square error perform well for a wide class of distributions. [ABSTRACT FROM AUTHOR]

The high quality and efficient production of greenhouse vegetation depend on micrometeorology environmental adjusting such as system warming and illumination supplement. In order to improve the quantity, quality, and efficiency of greenhouse vegetation, it is necessary to figure out the relationship between the crop growth conditions and environmental meteorological factors, which could give constructive suggestions for precise control of the greenhouse environment and reduce the running costs. The parameters from the color information of the plant canopy reflect the internal physiological conditions, thus, the RGB model has been widely used in the color analysis of digital pictures of leaves. We take photographs of Begonia Fimbristipula Hance (BFH) growing in the greenhouse at a fixed time every day and measure the meteorological factors. The results showed that the color scale for the single leaf, single plant, and the populated canopy of the BFH photographs all have skewed cumulative distribution histograms. The color gradation skewness-distribution (CGSD) parameters of the RGB model were increased from 4 to 20 after the skewness analysis, which greatly expanded the canopy leaf color information and could simultaneously describe the depth and distribution characteristics of the canopy color. The 20 CGSD parameters were sensitive to the micrometeorology factors, especially to the radiation and temperature accumulation. The multiple regression models of mean, median, mode, and kurtosis parameters to microclimate factors were established, and the spatial models of skewness parameters were optimized. The models can well explain the response of canopy color to microclimate factors and can be used to monitor the variation of plant canopy color under different micrometeorology.

Background: Little is known about how different outlier estimation methods affect cutoff limits for outliers in single fiber electromyography. Methods: We compared in a prospective fashion the established 18th jitter value (18thjv) method to three, whole‐distribution based, outlier detection methods: the interquartile range (IQR), the log‐normal, and the Z‐score method. The reference limits were probed in a normal cohort and in myasthenia gravis (MG) patients. Results: Differences in outlier cutoff values between the different methods were in the range of 2 μs. The number of abnormal muscles according to the computed criteria was similar for all four methods in the control group. Classification metrics (sensitivity, specificity, Youden's statistic, and predictive values) were also similar among the different methods. In the MG group, however, the Z‐score method failed to identify the abnormal jitter values. Accordingly, Kappa agreement was substantial to perfect (0.658 to 1) between the three methods (18thjv, IQR, and log‐normal), but was equivalent to chance between the three methods and the Z‐score in the MG group. Conclusions: The established 18thjv method proved largely robust when compared to whole‐distribution based methods, and its use in clinical practice is justified. Simple estimation of outlier limits by adding two SDs to the mean of the data, leads to unacceptable deviations from the true cutoff values. Moreover, in a clinical scenario in which the final electrodiagnosis depends only on the number of outliers, it is meaningful to accept a tolerance zone of about 2 μs, which is the approximate variation range among the different methods. [ABSTRACT FROM AUTHOR]

We focus on the normal approximation for point estimation of the ratios of medians of two independent, log-normal distributions. We investigate its performance in terms of bias, variance, and mean square error, using Monte Carlo simulations. The results show that the normal approximation, which is relatively simple, provides a reliable result. The normal approximation approaches could be recommended on the basis of the specific values of the parameters and/or sample sizes. The point estimation is illustrated using real data examples. [ABSTRACT FROM AUTHOR]

Skewed citation distribution is a major limitation of the Journal Impact Factor (JIF) representing an outlier-sensitive mean citation value per journal The present study focuses primarily on this phenomenon in the medical literature by investigating a total of n = 982 journals from two medical categories of the Journal Citation Report (JCR). In addition, the three highest-ranking journals from each JCR category were included in order to extend the analyses to non-medical journals. For the journals in these cohorts, the citation data (2018) of articles published in 2016 and 2017 classified as citable items (CI) were analysed using various descriptive approaches including e.g. the skewness, the Gini coefficient, and, the percentage of CI contributing 50% or 90% of the journal's citations. All of these measures clearly indicated an unequal, skewed distribution with highly-cited articles as outliers. The %CI contributing 50% or 90% of the journal's citations was in agreement with previously published studies with median values of 13–18% CI or 44–60% CI generating 50 or 90% of the journal's citations, respectively. Replacing the mean citation values (corresponding to the JIF) with the median to represent the central tendency of the citation distributions resulted in markedly lower numerical values ranging from − 30 to − 50%. Up to 39% of journals showed a median citation number of zero in one medical journal category. For the two medical cohorts, median-based journal ranking was similar to mean-based ranking although the number of possible rank positions was reduced to 13. Correlation of mean citations with the measures of citation inequality indicated that the unequal distribution of citations per journal is more prominent and, thus, relevant for journals with lower citation rates. By using various indicators in parallel and the hitherto probably largest journal sample, the present study provides comprehensive up-to-date results on the prevalence, extent and consequences of citation inequality across medical and all-category journals listed in the JCR. [ABSTRACT FROM AUTHOR]

Left‑censored data occur frequently in many areas. At present, researchers pay attention to skewed censored distributions more frequently. This paper deals with statistical inference of type I multiply left‑censored Weibull and exponential distributions. It suggests a computational procedure for calculation of maximum likelihood estimates of the parameters. The expected Fisher information matrix for estimation of variances of estimated parameters is introduced. The estimates are then used for construction of confidence intervals for the expectation using the maximum likelihood method. Asymptotic tests for comparison of distributions (expectations respectively) of two independent left‑censored Weibull samples are proposed. Furthermore, asymptotic tests for assessing suitability of reduction of the Weibull distribution to the exponential distribution are introduced. Finally, the left‑censored exponential distribution is briefly described. Methods derived in this paper are illustrated on elemental carbon measurements, and can be applied in analysis of real environmental and/or chemical data.

Nearly all distributions in bibliometrics are skewed. In particular, the distribution of citations of publications by research units is skewed. In a statistical view, the calculation of mean values can imply misleading or even wrong information. However, in citation analysis, the calculation of mean values of skewed distributions are standard. Therefore, when ranking research units, it is recommended instead to replace the calculation of standard mean values by the calculation of adjusted mean values to exclude outliers with very high citations and those with very few or no citations as well. Such an adjusted mean value is oriented on the standard activity of a research unit and results in a more adequate assessment. This approach is based on the Hirsch-index concept. The calculation results in a different ranking of research units, which may be important in cases where the distribution of finances depends on bibliometric rankings. In addition, a differentiation between standard activities and excellent results is possible, thus opening two dimensions of the assessment of research units. [ABSTRACT FROM AUTHOR]

In many statistical analysis, data may consist of excess zero values and the non-zero values are highly positively skewed. Confidence intervals based on a normal approximation for such zero-inflated data may have low coverage probabilities. An empirical likelihood (EL) and adjusted empirical likelihood methods are proposed to construct a non-parametric confidence interval for the mean of zero-inflated population, which are very simple and easy to implement. These EL confidence intervals were compared with existing confidence intervals. Simulation studies are carried out. Finally, the method is implemented in a real data set. [ABSTRACT FROM AUTHOR]

The expressivity of machine learning algorithms is considered to be critical in intelligent data analysis tasks for practical application. As an alternative set of classification rule learning algorithms to conventional decision tree, Prism family of algorithms induce modular rules concisely, thus exhibiting good expressiveness for human users. However, existing Prism rule induction techniques are limited by the assumption of Gaussian distribution for quantitative attributes, and may not be available for real life data analyzing, in which skewness is commonly observed. For this reason, we investigate a skew-adaptive mechanism for rule term boundary delimitation in Prism inductive learning. The propose algorithm, called P2-Prism, could learn expressive classification rules directly from quantitative data beyond Gaussian distribution. By employing statistical inference characteristics of Poisson process, our mechanism provides a significant contribution to classification rule inductive learning with adaption of skewed data distribution. The experimental evaluation of our algorithm demonstrates its skew-adaptive superiority on benchmark datasets, comparing with state-of-the-art algorithms. Furthermore, it is shown that P2-Prism is a robust classifier in the presence of various levels of noise, which further reveals its adaptability to the skewness of data distribution. [ABSTRACT FROM AUTHOR]

Background: Image processing techniques have been widely used in the analysis of leaf characteristics. Earlier techniques for processing digital RGB color images of plant leaves had several drawbacks, such as inadequate de-noising, and adopting normal-probability statistical estimation models which have few parameters and limited applicability. Results: We confirmed the skewness distribution characteristics of the red, green, blue and grayscale channels of the images of tobacco leaves. Twenty skewed-distribution parameters were computed including the mean, median, mode, skewness, and kurtosis. We used the mean parameter to establish a stepwise regression model that is similar to earlier models. Other models based on the median and the skewness parameters led to accurate RGB-based description and prediction, as well as better fitting of the SPAD value. More parameters improved the accuracy of RGB model description and prediction, and extended its application range. Indeed, the skewed-distribution parameters can describe changes of the leaf color depth and homogeneity. Conclusions: The color histogram of the blade images follows a skewed distribution, whose parameters greatly enrich the RGB model and can describe changes in leaf color depth and homogeneity. [ABSTRACT FROM AUTHOR]

Control chart has been long-established among the highly reputable tools in statistical process control (SPC) with extensive industrial application. Shewhart chart is one of the most popular charts, but its reliability is arguable when dealing with skewed data, due to inflated false alarm rate (Type I error). In alleviating the problem, this study has developed a new X-bar control chart for monitoring of process mean using skewness correction (SC) method for skewed distributions, thus named as SCS X control chart. The SC method is incorporated into the standard Shewhart's X-bar chart, leading to the proposed univariate SCS X to monitor the process mean of skewed data. It offers asymmetric control limits using the usual three sigma and the same known function of the skewness estimated from subgroups without assuming any distribution. The chart's constants, and skewness correction factor are computed via numerical integration. To evaluate the strength and weakness of the charts, several conditions are created from different types of distributions and subgroup sizes. The SCS X performance evaluation based on the false alarm rates (FAR) and probability of out-of-control (OOC) detection are accomplished using Monte Carlo simulation in SAS version 9.4. To illustrate its applicability, a real data on healthcare is employed. Its FAR performance is compared to the established charts: weighted variance X-bar R (WV- ); weighted variance X-bar S (WVS X ); and standard X-bar S (STS X ). In aspect of the probability of OOC detection, the SCS X is contended by the exact S chart. Extensive simulation study shows that the proposed SCS X chart performs well in terms of FAR in almost all the degrees of skewness and sample sizes, n . In terms of the probability of OOC detection, it provides the closest values to those of the exact chart. It offers substantial enhancement over the established charts, and thus signifies as a preferred alternative especially in cases of skewed data. [ABSTRACT FROM AUTHOR]

A finite-step procedure is proposed for maximum likelihood estimation of the three-parameter asymmetric Laplace distribution. Its performance is compared with the iterative method most commonly used for this distribution. The new procedure is much faster and reliably identifies samples for which maximum likelihood estimates lie on the boundary of the parameter space, making it a good choice for simulation studies and simulation-based methodologies. [ABSTRACT FROM AUTHOR]

Random variables in biology, social and health sciences commonly follow skewed distributions. Many of these variables can be represented by exGaussian functions; however, in practice, they are sometimes considered as Gaussian functions when statistical analysis is carried out. The asymmetry can play a fundamental role which can not be captured by central tendency estimators such as the mean. By means of Monte Carlo simulations, the effect of a small asymmetry in the generating functions of the chi distribution is studied. To this end, the k generating functions are taken as exGaussian functions. The limits of this approximation are tested numerically for the practical case of three health-related variables: one physical (body mass index) and two cognitive (verbal fluency and short-term memory). This work is in line with our previous works on a physics-inspired mathematical model to represent the reaction times of a group of individuals.

In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this article, we study a class of skewed distributions by invoking skewness into some known distributions. In particular, we consider using the logistic kernel to derive a class of univariate distribution called the truncated-logistic skew symmetric (TLSS) distribution. We provide some structural properties of the proposed distribution and develop the statistical inference for the TLSS distribution. A simulation study is conducted to investigate the efficacy of the maximum likelihood method. For illustrative purposes, two real data sets from environmental studies are used to exhibit the applicability of such a model. [ABSTRACT FROM AUTHOR]

The heavy metal concentration of soil samples often exhibits a skewed distribution, especially for soil samples from mining areas with an extremely high concentration of heavy metals. In this study, to model soil contamination in mining areas using reflectance spectroscopy, the skewed distribution was corrected and heavy metal concentration estimated. In total, 46 soil samples from a mining area, along with corresponding field soil spectra, were collected. Laboratory spectra of the soil samples and the field spectra were used to estimate copper (Cu) concentration in the mining area. A logarithmic transformation was used to correct the skewed distribution, and based on the sorption of Cu on spectrally active soil constituents, the spectral bands associated with iron oxides were extracted from the visible and near-infrared (VNIR) region and used in the estimation. A genetic algorithm was adopted for band selection, and partial least squares regression was used to calibrate the estimation model. After transforming the distribution of Cu concentration, the accuracies (R2) of the estimation of Cu concentration using laboratory and field spectra separately were 0.94 and 0.96. The results indicate that Cu concentration in the mining area can be estimated using reflectance spectroscopy following correction of skewed distribution. Image 1 • Skewed distribution hinders the estimation of heavy metal concentration in soil. • The natural logarithm transformation corrects the highly skewed distribution. • A selected spectral subset is beneficial to the estimation of Cu concentration. • Spectroscopic method is feasible to investigate soil heavy metal concentration. Capsule : Reflectance spectroscopy of soil could be an alternative to investigate heavy metal concentration in mining areas. [ABSTRACT FROM AUTHOR]

Tukey's control chart is generally used for monitoring the processes where the measurement process physically damages the product. It is based on single observation and robust to outliers. In this paper, two optimal synthetic Tukey's control charts are proposed by integrating the conforming run length chart with the Tukey's control chart and its modification. The performance comparison of the proposed charts with the existing Tukey's control charts is made by using out-of-control average run length and extra quadratic loss as performance metrics. The proposed charts offer better protection against the process shifts as compare to the existing Tukey's control charts when the underlying process distribution is symmetric or asymmetric. Simulation studies also establish the supremacy of the proposed control charts over the existing Tukey's control charts. In the end, an illustrative example based on a real data set of the combined cycle power plant is provided for practical implementation. [ABSTRACT FROM AUTHOR]

High anomalous grades are very common in gold deposits, whose presence requires careful treatment to prevent overestimation of metal content. Mineral resource analysts have worked on the estimation of several gold deposits, and none of the classical methods were able to avoid manual interventions, such as cutting high grades for local estimation or using more information beyond the data for the variogram inference. The Field Parametric Geostatistics (FPG) is presented as an alternative for the application of linear kriging methods to estimate highly skewed distributions, proposing a mathematical model which incorporates the grades and its representativeness into a new variable, reducing the influence of high grades without empirical manual interventions. In this article, the mathematical formulation of the FPG theory is presented, as well as its application in datasets with outliers and high skewed distributions: the Walker Lake dataset and the Amapari gold deposit. The results are compared to results obtained by the application of standard techniques, demonstrating that FPG is a feasible alternative to estimate local grades and local reserves for highly skewed variables. [ABSTRACT FROM AUTHOR]

This paper presents a method for feature selection in a high-dimensional classification context. The proposed method finds a candidate solution based on quality criteria using subset searching. In this study, the competitive swarm optimization (CSO) algorithm was implemented to solve feature selection problems in high-dimensional data. A new asymmetric chaotic function was proposed and used to generate the population and search for a CSO solution. Its histogram is right-skewed. The proposed method is named an asymmetric chaotic competitive swarm optimization algorithm (ACCSO). According to the asymmetrical property of the proposed chaotic map, ACCSO prefers zero than one. Therefore, the solution is very compact and can achieve high classification accuracy with a minimal feature subset for high-dimensional datasets. The proposed method was evaluated on 12 datasets, with dimensions ranging from 4 to 10,304. ACCSO was compared to the original CSO algorithm and other metaheuristic algorithms. Experimental results show that the proposed method can increase accuracy and it reduces the number of selected features. Compared to different optimization algorithms with other wrappers, the proposed method exhibits excellent performance.

Data stream learning in non-stationary environments and skewed class distributions has been receiving more attention in machine learning communities. This paper proposes a novel ensemble classification method (ECSDS) for classifying data streams with skewed class distributions. In the proposed ensemble method, back-propagation neural network is selected as the base classifier. In order to demonstrate the effectiveness of our proposed method, we choose three baseline methods based on ECSDS and evaluate their overall performance on ten datasets from UCI machine learning repository. Moreover, the performance of incremental learning is also evaluated by these datasets. The experimental results show our proposed method can effectively deal with classification problems on non-stationary data streams with class imbalance. [ABSTRACT FROM AUTHOR]

The standard small area estimator, the empirical best linear unbiased predictor (EBLUP), estimates small area parameters by way of linear mixed models. The EBLUP assumes normal and independent random small area effects as well as normal and independent random sampling errors. Under these assumptions, the variable of interest also follows a normal distribution. In practice, however, the above assumptions are often violated. The variable of interest is often non-normal and highly skewed, and the small areas are frequently spatially dependent. In this paper, we propose the spatial empirical Bayes predictor (SEBP) of the small area mean of a positively skewed variable of interest in the presence of spatial dependence among the random small area effects. We assume that the variable of interest follows a normal distribution after a log transformation and that its log transform is linked to some auxiliary variables by a nested error regression model. The SEBP is derived under the log-transformed nested error regression model. By way of simulation, we show that compared to its alternatives, i.e., the direct estimator which is solely based on the survey data for the small area under study, the EBLUP which does not take into account spatial dependence and skewness, the empirical Bayes predictor which takes into account skewness but not spatial dependence among the small areas, the SEBP has the smallest average relative bias and average relative root-mean-squared error for various combinations—though not all—of skewness and spatial correlation. [ABSTRACT FROM AUTHOR]

The growing scholarly interest in research top performers comes from the growing policy interest in research top performance itself. A question emerges: what makes someone a top performer? In this paper, the upper 10% of Polish academics in terms of research productivity are studied, and predictors of entering this class are sought. In the science system (and Poland follows global patterns), a small number of scholars produce most of the works and attract huge numbers of citations. Performance determines rewards, and small differences in talent translate into a disproportionate level of success, leading to inequalities in resources, research outcomes, and rewards. Top performers are studied here through a bivariate analysis of their working time distribution and their academic role orientation, as well as through a model approach. Odds ratio estimates with logistic regression of being highly productive Polish academics are presented. Consistently across major clusters of academic disciplines, the tiny minority of 10% of academics produces about half (44.7%) of all Polish publications (48.0% of publications in English and 57.2% of internationally co-authored publications). The mean research productivity of top performers across major clusters is on average 7.3 times higher than that of the other academics, and in terms of internationally co-authored publications, 12.07 times higher. High inequality was observed: the average research productivity distribution is highly skewed with a long tail on the right not only for all Polish academics but also for top performers. The class of top performers is as internally stratified as that of their lower-performing colleagues. Separate regression models for all academics, science, technology, engineering and mathematics academics, and social sciences and humanities academics are built based on a large national sample (2525 usable observations), and implications are discussed. [ABSTRACT FROM AUTHOR]

The problem of estimation is motivated by some studies from the area of developmental programs management to be implemented by the government and non-government organizations under different phases. The examples of such programs are educational programs, women empowerment programs for enhancing gross enrollment ratio in a region. There are two important variables in such programs. One of the variables is called the survey variable. The survey variable changes under the impact of the program over different phases and is termed as the response variable. In our study, we consider linear impacts of the programs under successive phases and multiplicative model which relates the response and survey variables. The management of the programs is interested in estimation of the mean of the response variable. Therefore, in this paper, we propose an unbiased estimator of the population mean of the response variable by using ranked set sampling procedure on the survey variable. The estimator is then compared with the estimator based on simple random sample (SRS). The relative precisions of the proposed estimator with the estimator based on SRS are computed for some symmetric and skew distributions. It is shown that the gains in relative precisions of the proposed estimator are substantial for all sample sizes and the chosen distributions. We applied the formulas derived in this paper to one real life example from India's report, Education for all towards quality with equity, of National University of Education Planning and Administration, New Delhi, 2014. [ABSTRACT FROM AUTHOR]