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Time series of proportions are often encountered in applications such as ecology, environmental science and public health. Strategies for such data include linear regression after logistic transformation. Though easy to fit, the transformation approach renders covariate effects uninterpretable on the scale on which they were observed owing to Jensen's inequality. An alternative to the transformation approach has been to directly model the response via the beta distribution. In this paper, we extend zero-inflated beta regression models for independent proportions to time series data that is bounded over the unit interval and that may take on zero values. Estimation is within the partial-likelihood framework and is computationally feasible to implement. We outline the asymptotic theory of our maximum partial likelihood estimators under mild regularity conditions and investigate their bias and variability using simulation studies. The utility of our method is illustrated using two real data examples. [ABSTRACT FROM AUTHOR]

Compositional data (CoDa) often appear in various fields such as biology, medicine, geology, chemistry, economics, ecology and sociology. Although existing Dirichlet and related models are frequently employed in CoDa analysis, sometimes they may provide unsatisfactory performances in modelling CoDa as shown in our first real data example. First, this paper develops a multivariate compositional inverse Gaussian (CIG) model as a new tool for analysing CoDa. By incorporating the stochastic representation (SR), the expectation–maximization (EM) algorithm (aided by a one-step gradient descent algorithm) can be established to solve the parameter estimation for the proposed distribution (model). Next, zero observations may be often encountered in the real CoDa analysis. Therefore, the second aim of this paper is to propose a new model (called as ZCIG model) through a novel mixture SR based on both the CIG random vector and a so-called zero-truncated product Bernoulli random vector to model CoDa with zeros. Corresponding statistical inference methods are also developed for both cases without/with covariates. Two real data sets are analysed to illustrate the proposed statistical methods by comparing the proposed CIG and ZCIG models with existing Dirichlet and logistic-normal models. [ABSTRACT FROM AUTHOR]

This paper, based on the E-Bayesian estimation (expected Bayesian estimation), introduced the definition of E-posterior risk (expected posterior risk); we will derive the expressions of E-Bayesian estimation and their E-posterior risk for failure probability under the compound symmetric LINEX loss function, and will compare the results with the corresponding results under the square loss function. Monte Carlo simulations compared the performances of the proposed the estimation method, and compared the results on the basis of E-posterior risk. Finally, combined with the life testing data from a type of aero engine, the calculation and reliability analysis are performed, with E-Bayesian estimation and hierarchical Bayesian estimation, respectively (also using the MCMC method). When considering evaluating the E-Bayesian estimations under different loss functions, in this paper the E-posterior risk as an the evaluation standard is proposed. [ABSTRACT FROM AUTHOR]

In this paper, statistical inferences for the parameters, reliability, and failure rate functions (as parameters) of the exponentiated Kies distribution are accomplished using maximum likelihood and both Lindley and Markov chain Monte Carlo techniques, under adaptive Type-II progressive censoring. Depending on the Fisher information matrix and the delta method, we find the approximate confidence intervals for the parameters and the reliability and failure rate functions, respectively. Furthermore, the samples generated from Markov chains Monte Carlo are used to generate credible intervals for the parameters, reliability, and failure rates functions. Symmetric and asymmetric loss functions are also used to find Bayes estimators using Markov chain Monte Carlo and Lindley techniques. Comparisons between the two techniques of evaluation for different estimators under different sizes of data sets are conducted. Finally, a real-life example is applied to clarify the results of the used techniques. [ABSTRACT FROM AUTHOR]

Poisson distribution is a classic choice for modelling unbounded count data. However, count data arising in various fields of scientific research often have excess zeros and are under-reported. In such situations, Poisson distribution gives a poor fit and Poisson model based inferences lead to biased estimators and inaccurate confidence intervals. In this paper we develop a flexible model which can accommodate excess zeros and undercount. Internal validation data has been used for making likelihood based inferences. The impact of ignoring undercount and excess zeros are studied through extensive simulations. The finite sample behaviour of the estimators are investigated through bootstrap methodology. Finally, a real life data which is supposedly under-reported and known to have excess zeros is analysed. [ABSTRACT FROM AUTHOR]

Maji et al. [Robust statistical inference based on the C-divergence family. Ann Inst Stat Math. 2019;71:1289–1322] introduced the minimum C-divergence estimators and plugging them in the C-divergence measures give test statistics for testing simple null and composite null hypotheses. One inconvenience of these test statistics is that their asymptotic distribution is not, in general, a chi-square distribution but a linear combination of chi-square distributions. To overcome this inconvenience, in this paper we consider Wald-type test statistics based on minimum C-divergence estimators. We establish that this family of test statistics is a chi-square distribution and we get an approximation of the power function under simple null hypothesis and composite null hypothesis. We have calculated both first order and second order influence function of the Wald-type test statistics and based on it we can see the robustness of the family of test statistics considered in this paper. Both simulated and real data examples have been shown as part of numerical results. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce a new family of distributions, namely compound zero-truncated Poisson exponential distribution of which exponential distribution is a special case. The proposed family of distributions represents the zero truncated-Poisson sum of independent and identically distributed exponential random variables. The proposed distribution has two parameters and its probability density function can be skewed and unimodal. It can be used quite effectively in analyzing skewed data. We suggest to use expectation–maximization (EM)-type algorithm to estimate the unknown parameters, and it is observed that it is easy to implement in practice. We further consider the bivariate version of the proposed model which has three parameters and provides different properties. We have performed extensive simulation studies to see the performances of the proposed EM algorithm, and a real data set has been analyzed to see the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

In both Tweedie and geometric Tweedie models, the common power parameter p ∉ (0 , 1) works as an automatic distribution selection. It separates two subclasses of semicontinuous (12) ones; and two datasets for illustration purposes are investigated. [ABSTRACT FROM AUTHOR]

The two-parameter Birnbaum–Saunders distribution was derived to describe the failure time from a process of fatigue crack growth. The scale parameter is also the median of the distribution. The inferences for the median of the distribution are mostly based on the maximum likelihood methods and subject to large-sample requirements. In this paper, we develop the exact small-sample confidence intervals of the median of the distribution when the shape parameter is known and unknown, respectively. Moreover, an alternative consistent estimator with an explicit form for the median of the distribution is provided in this study. Finally, we develop the hypothesis testing for the median of the distribution based on a small sample. The Monte Carlo simulations are further carried out to prove the power of the proposed test well performance. [ABSTRACT FROM AUTHOR]

In this study, we discuss the problem of estimating ρ = P (X > Y) , when X and Y are two independent power Lindley random variables, based on progressively type II right censored order statistics. The maximum likelihood estimator of ρ and its asymptotic distribution, asymptotic interval estimator of ρ, Bayesian point estimators for ρ under symmetric and asymmetric loss functions as well as credible intervals for ρ are achieved when X and Y have a common parameter. Since it seems that the integrals pertaining to the Bayes estimation cannot be obtained in explicit forms, we propose the Metropolis-Hastings within Gibbs algorithm to find the approximate Bayes estimates of ρ. A simulation study is given in order to evaluate the proposed estimators and compare the different methods, developed in the paper. The corresponding results for the general case (when X and Y have no common parameters), as well as two examples, are also provided. The paper finishes with some remarks. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and non-parametric inference. In this paper, we consider RSS-based estimation for the two-parameter Birnbaum–Saunders (BS) distribution, which is widely used in reliability analysis. The estimation methods considered for comparison purposes were: maximum likelihood (ML), modified method of moments (MMM), maximum product of spacings (MPS), and Anderson–Darling (AD). The performance of the RSS-based estimators was evaluated through Monte Carlo simulations under both perfect and imperfect ranking assumptions. The bias, mean squared error, and mean integrated squared error were used as the criteria for comparison. The results revealed that the RSS-based estimators perform better than their simple random sampling (SRS) counterparts. The ML estimator performed the best under the perfect ranking assumption, while the MMM provided better performance for higher levels of imperfect ranking. Additional simulations based on data from a forest inventory corroborated our findings. [ABSTRACT FROM AUTHOR]

In this paper, we consider maximum likelihood estimation of the proportional parameter in a proportional hazard rate (PHR) model based on single and multiply censored order statistics, and progressively Type-II censored order statistics from lifetimes that follow the PHR model. The expectation-maximization (EM) algorithm is proposed for computing the maximum likelihood estimate (MLE) by utilizing the relationship between order statistics and lifetimes of components in a system. The existence and uniqueness of the MLE under different data structures are discussed. We also propose a reliable initial value for the iterative algorithm based on approximating the likelihood function using Taylor series expansion. Monte Carlo simulation studies are used to study the performance of the proposed EM algorithms and the proposed initial value. The proposed EM approach is shown to be a good alternative to the Newton-Raphson method in terms of computational efficient and robustness to the initial value. We also show that the proposed initial value works well with the EM algorithm in obtaining the MLE. [ABSTRACT FROM AUTHOR]

This paper studies the E-Bayesian estimations and their E-MSE of Pareto distribution parameter under different loss functions. In order to measure the estimated error, in the case of the two hyper parameters, the definition of E-MSE (expected mean square error) is introduced based on the definition of E-Bayesian estimation, and the formulas of E-Bayesian estimation and the formulas of E-MSE are given, respectively. Monte Carlo simulations are performed to analysis the performances of the proposed methods, results are compared on the basis of E-MSE. Finally, combined with the golfers income problem are performed to calculated, the maximum likelihood estimations of the shape parameter and scale parameter are given, respectively, and that compared and analysed with the E-Bayesian estimations; moreover, the Bayesian credible intervals of the shape parameter and scale parameter are also given, respectively, by MCMC method. [ABSTRACT FROM AUTHOR]

This paper deals with random sign-censoring data (RSCD) which may be observed under repair alert models (RAMs) for implementing age-dependent maintenance policies on engineering devices. A general family for lifetime distributions of devices is considered and estimates of parameters are derived on the basis of RSCD via the likelihood and the Bayesian approaches. In recent literature, the cumulative repair alert function (CRAF), denoted by, of the RAMs is considered proportional to the cumulative hazard rate function of the device lifetime. This paper also suggests a polynomial form for the CRAFfor modelling purposed. A comparison between the two kinds of CRAFs under the RAMs is given for a real data set from Mendenhall and Hader [Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika. 1958;45:504–520] The data are times to failure for a type of communication transmitter-receivers of a single commercial airline. Some special cases including exponential, Weibull and Pareto distributions are studied in a great detail. [ABSTRACT FROM PUBLISHER]

As an applicable and flexible lifetime model, the two-parameter generalized half-normal (GHN) distribution has been received wide attention in the field of reliability analysis and lifetime study. In this paper maximum likelihood estimates of the model parameters are discussed and we also proposed corresponding bias-corrected estimates. Unweighted and weighted least squares estimates for the parameters of the GHN distribution are also presented for comparison purpose. Moreover, the likelihood ratio test is provided as complementary. Simulation study and illustrative examples are provided to compare the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) is an efficient method for estimating parameters when exact measurement of observation is difficult and/or expensive. In this paper, we provide maximum likelihood estimation of the shape and scale parameters concerning generalized Rayleigh distribution based on RSS and its some modifications. We compare the biases, mean squared errors and relative efficiencies of estimators in simple random sampling, RSS, extreme RSS and median RSS with different set and cycle sizes. Comparison of the mean squared errors of estimators in RSS for the case of imperfect ranking are also given. Monte Carlo simulation study is performed by using Mathematica 11.0 with 10,000 repetitions. [ABSTRACT FROM AUTHOR]

In this paper, two new statistics based on comparison of the theoretical and empirical distribution functions are proposed to test exponentiality. Critical values are determined by means of Monte Carlo simulations for various sample sizes and different significance levels. Through an extensive simulation study, 50 selected exponentiality tests are studied for a wide collection of alternative distributions. From the empirical power study, it is concluded that, firstly, one of our proposals is preferable for IFR (increasing failure rate) and UFR (unimodal failure rate) alternatives, whereas the other one is preferable for DFR (decreasing failure rate) and BFR (bathtub failure rate) alternatives and, secondly, the new tests can be considered serious and powerful competitors to other existing proposals, since they have the same (or higher) level of performance than the best tests in the statistical literature. [ABSTRACT FROM PUBLISHER]

In this paper, statistical inferences for the size-biased Weibull distribution in two different cases are drawn. In the first case where the sizerof the bias is considered known, it is proven that the maximum-likelihood estimators (MLEs) always exist. In the second case where the sizeris considered as an unknown parameter, the estimating equations for the MLEs are presented and the Fisher information matrix is found. The estimation with the method of moments can be utilized in the case the MLEs do not exist. The advantage of treatingras an unknown parameter is that it allows us to perform tests concerning the existence of size-bias in the sample. Finally a program in Mathematica is written which provides all the statistical results from the procedures developed in this paper. [ABSTRACT FROM PUBLISHER]

In this paper, E-Bayesian and hierarchical Bayesian estimations of the shape parameter, when the underlying distribution belongs to the proportional reversed hazard rate model, are considered. Maximum likelihood, Bayesian and E-Bayesian estimates of the unknown parameter and reliability function are obtained based on record values. The Bayesian estimates are derived based on squared error and linear–exponential loss functions. It is pointed out that some previously obtained order relations of E-Bayesian estimates are inadequate and these results are improved. The relationship between E-Bayesian and hierarchical Bayesian estimations is obtained under the same loss functions. The comparison of the derived estimates is carried out by using Monte Carlo simulations. A real data set is analysed for an illustration of the findings. [ABSTRACT FROM AUTHOR]

Tweedie regression models (TRMs) provide a flexible family of distributions to deal with non-negative right-skewed data and can handle continuous data with probability mass at zero. Estimation and inference of TRMs based on the maximum likelihood (ML) method are challenged by the presence of an infinity sum in the probability function and non-trivial restrictions on the power parameter space. In this paper, we propose two approaches for fitting TRMs, namely quasi-likelihood (QML) and pseudo-likelihood (PML). We discuss their asymptotic properties and perform simulation studies to compare our methods with the ML method. We show that the QML method provides asymptotically efficient estimation for regression parameters. Simulation studies showed that the QML and PML approaches present estimates, standard errors and coverage rates similar to the ML method. Furthermore, the second-moment assumptions required by the QML and PML methods enable us to extend the TRMs to the class of quasi-TRMs in Wedderburn's style. It allows to eliminate the non-trivial restriction on the power parameter space, and thus provides a flexible regression model to deal with continuous data. We provide an R implementation and illustrate the application of TRMs using three data sets. [ABSTRACT FROM AUTHOR]

The generalized lognormal distribution plays an important role in analysing data from different life testing experiments. In this paper, we consider Bayesian analysis of this distribution using various objective priors for the model parameters. Specifically, we derive expressions for the Jeffreys-type priors, the reference priors with different group orderings of the parameters, and the first-order matching priors. We also study the properties of the posterior distributions of the parameters under these improper priors. It is shown that only two of them result in proper posterior distributions. Numerical simulation studies are conducted to compare the performances of the Bayesian estimators under the considered priors and the maximum likelihood estimates. Finally, a real-data application is also provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

Recently, Ristić and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. The method of maximum likelihood is used to estimate the model parameters. We illustrate the flexibility of the new distribution by means of three applications to real life data sets. [ABSTRACT FROM PUBLISHER]

Asymmetric models have been discussed quite extensively in recent years, in situations where the normality assumption is suspected due to lack of symmetry in the data. Techniques for assessing the quality of fit and diagnostic analysis are important for model validation. This paper presents a study of the mean-shift method for the detection of outliers in regression models under skew scale-mixtures of normal distributions. Analytical solutions for the estimators of the parameters are obtained through the use of Expectation–Maximization algorithm. The observed information matrix for the calculation of standard errors is obtained for each distribution. Simulation studies and an application to the analysis of a data have been carried out, showing the efficiency of the proposed method in detecting outliers. [ABSTRACT FROM PUBLISHER]

In reliability theory, risk analysis, renewal processes and actuarial studies, the residual lifetimes data play an important essential role in studying the conditional tail of the lifetime data. In this paper, based on some observed ordered residual Weibull data, we introduce different prediction methods for obtaining prediction intervals (PIs) of future residual lifetimes including likelihood, Wald, moments, parametric bootstrap, and highest conditional methods. Monte Carlo simulations are performed to compare the performances of the so obtained PIs and one data analysis is performed for illustration purposes. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new method of estimation for the parameters and quantiles of the three-parameter Weibull distribution based on Type-II right censored data. The method, based on a data transformation, overcomes the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators are also consistent over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method of estimation performs well compared to some prominent methods in terms of bias and root mean squared error in small-sample situations. Finally, two real data sets are used to illustrate the proposed method of estimation. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a method of estimation of parameters and quantiles of the three-parameter gamma distribution based on Type-II right-censored data. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs well compared with another prominent method of estimation in terms of bias and root mean-squared error in small-sample situations. Finally, two real data sets are used for illustrating the proposed method. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to study the estimation of the reliabilityR=P(X

Exact confidence intervals for variances rely on normal distribution assumptions. Alternatively, large-sample confidence intervals for the variance can be attained if one estimates the kurtosis of the underlying distribution. The method used to estimate the kurtosis has a direct impact on the performance of the interval and thus the quality of statistical inferences. In this paper the author considers a number of kurtosis estimators combined with large-sample theory to construct approximate confidence intervals for the variance. In addition, a nonparametric bootstrap resampling procedure is used to build bootstrap confidence intervals for the variance. Simulated coverage probabilities using different confidence interval methods are computed for a variety of sample sizes and distributions. A modification to a conventional estimator of the kurtosis, in conjunction with adjustments to the mean and variance of the asymptotic distribution of a function of the sample variance, improves the resulting coverage values for leptokurtically distributed populations. [ABSTRACT FROM AUTHOR]

Longitudinal or clustered response data arise in many applications such as biostatistics, epidemiology and environmental studies. The repeated responses cannot in general be assumed to be independent. One method of analysing such data is by using the generalized estimating equations (GEE) approach. The current GEE method for estimating regression effects in longitudinal data focuses on the modelling of the working correlation matrix assuming a known variance function. However, correct choice of the correlation structure may not necessarily improve estimation efficiency for the regression parameters if the variance function is misspecified [Wang YG, Lin X. Effects of variance-function misspecification in analysis of longitudinal data. Biometrics. 2005;61:413–421]. In this connection two problems arise: finding a correct variance function and estimating the parameters of the chosen variance function. In this paper, we study the problem of estimating the parameters of the variance function assuming that the form of the variance function is known and then the effect of a misspecified variance function on the estimates of the regression parameters. We propose a GEE approach to estimate the parameters of the variance function. This estimation approach borrows the idea of Davidian and Carroll [Variance function estimation. J Amer Statist Assoc. 1987;82:1079–1091] by solving a nonlinear regression problem where residuals are regarded as the responses and the variance function is regarded as the regression function. A limited simulation study shows that the proposed method performs at least as well as the modified pseudo-likelihood approach developed by Wang and Zhao [A modified pseudolikelihood approach for analysis of longitudinal data. Biometrics. 2007;63:681–689]. Both these methods perform better than the GEE approach. [ABSTRACT FROM AUTHOR]

The inverse Gaussian (IG) distribution, also known as the Wald distribution, is a long-tailed positively skewed distribution and a well-known lifetime distribution. In this paper, we propose an efficient method of estimation for the parameters and quantiles of the three-parameter IG distribution, which is based on statistics invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared with other prominent methods in terms of bias and variance. Finally, we present two illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, inference for the scale parameter of lifetime distribution of ak-unit parallel system is provided. Lifetime distribution of each unit of the system is assumed to be a member of a scale family of distributions. Maximum likelihood estimator (MLE) and confidence intervals for the scale parameter based on progressively Type-II censored sample are obtained. A β-expectation tolerance interval for the lifetime of the system is obtained. As a member of the scale family, half-logistic distribution is considered and the performance of the MLE, confidence intervals and tolerance intervals are studied using simulation. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution. We then discuss some properties of these estimators and show by means of a Monte Carlo simulation study that the proposed estimators perform better than some other prominent estimators in terms of bias and root mean squared error. Finally, we present two real-life examples to illustrate the method of inference developed here. [ABSTRACT FROM AUTHOR]

Lognormal distribution is one of the popular distributions used for modelling positively skewed data, especially those encountered in economic and financial data. In this paper, we propose an efficient method for the estimation of parameters and quantiles of the three-parameter lognormal distribution, which avoids the problem of unbounded likelihood, by using statistics that are invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared to other prominent methods in terms of both bias and mean-squared error. Finally, we present two illustrative examples. [ABSTRACT FROM PUBLISHER]

In this paper, the Gompertz model is extended to incorporate time-dependent covariates in the presence of interval-, right-, left-censored and uncensored data. Then, its performance at different sample sizes, study periods and attendance probabilities are studied. Following that, the model is compared to a fixed covariate model. Finally, two confidence interval estimation methods, Wald and likelihood ratio (LR), are explored and conclusions are drawn based on the results of the coverage probability study. The results indicate that bias, standard error and root mean square error values of the parameter estimates decrease with the increase in study period, attendance probability and sample size. Also, LR was found to work slightly better than the Wald for parameters of the model. [ABSTRACT FROM PUBLISHER]

In this paper, a nonlinear model with response variables missing at random is studied. In order to improve the coverage accuracy for model parameters, the empirical likelihood (EL) ratio method is considered. On the complete data, the EL statistic for the parameters and its approximation have a χ2asymptotic distribution. When the responses are reconstituted using a semi-parametric method, the empirical log-likelihood on the response variables associated with the imputed data is also asymptotically χ2. The Wilks theorem for EL on the parameters, based on reconstituted data, is also satisfied. These results can be used to construct the confidence region for the model parameters and the response variables. It is shown via Monte Carlo simulations that the EL methods outperform the normal approximation-based method in terms of coverage probability for the unknown parameter, including on the reconstituted data. The advantages of the proposed method are exemplified on real data. [ABSTRACT FROM AUTHOR]