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Abstract In this article, we have proposed memory-type exponential and non-exponential estimators for population variance based on exponentially weighted moving average (EWMA) statistic in stratified sampling. We drive mathematical expressions for mean square errors of the proposed estimators using Taylor and exponential expansions. Our analysis demonstrates that the proposed memory-type estimators outperform the conventional estimators under stratification, particularly, when the information of previous sample is utilized. The performances of the proposed estimators are evaluated mathematically by deriving the conditions in which the memory-type estimators would perform better than their corresponding conventional estimators under stratification. Through an extensive simulation, we evaluated the performance of the proposed estimators across various population parameters, revealing their enhanced efficiency in time-scaled survey. Additionally, a real data application is also used to support the mathematical findings, confirming the practical utility of the proposed estimators. The results of numerical study underscore the importance of the use of previous sampled information which significantly improves the accuracy and reliability of the proposed estimator for variance estimation for time-scaled surveys.

Abstract This paper offers a novel approach to formulate efficient ratio estimator of the population variance using a transformed auxiliary variable. The impact of transformation on auxiliary information has also been discussed. It is observed that incorporating a transformed auxiliary variable result in a high gain in efficiency. Theoretical properties of the newly developed estimators have been derived. The empirical and simulation studies show that the suggested estimators outperformed the existing estimators.

The endogeneity problem arises when the auxiliary variables correlate to the error terms. In such cases, appropriate instrumental variables ensure efficient estimation. Calibration has recognized itself as an important methodological tool at a large scale to estimate the population total in survey sampling. Which does not offer efficient estimation in the presence of endogeneity. When endogeneity is present in the auxiliary variables, the calibration using endogenous auxiliary variables may produce biasedness and increase variance due to inappropriate model assumptions. In this article, we propose instrumental-variable calibrated estimators by using the classical instrumental-variables approach for the case of exact identification that are more efficient than conventional calibration estimators when some auxiliary variables are endogenous. The necessary properties of the proposed estimators are presented. Our study is backed by both the simulation study and a real data example to check the performance of the proposed estimators.

Estimating dispersion in populations that are extremely rare, hidden, geographically clustered, and hard to access is a well-known challenge. Conventional sampling approaches tend to overestimate the variance, even though it should be genuinely reduced. In this environment, adaptive cluster sampling is considered to be the most efficient sampling technique as it provides generally a lower variance than the other conventional probability sampling designs for the assessment of rare and geographically gathered population parameters like mean, total, variance, etc. The use of auxiliary data is very common to obtain the precise estimates of the estimators by taking advantage of the correlation between the survey variable and the auxiliary data. In this article, we introduced a generalized estimator for estimating the variance of populations that are rare, hidden, geographically clustered and hard-to-reached. The proposed estimator leverages both actual and transformed auxiliary data through adaptive cluster sampling. The expressions of approximate bias and mean square error of the proposed estimator are derived up to the first-order approximation using Taylor expansion. Some special cases are also obtained using the known parameters associated with the auxiliary variable. The proposed class of estimators is compared with available estimators using simulation and real data applications.

Companies and organizations aim to improve the performance of their business processes to stay competitive. Recently, researchers have shown significant interest in process mining, particularly its ability to extract accurate information from process-related data. Process enhancement is a crucial aspect of process mining, involving the extraction of information from the actual process event log to extend or improve existing processes. Enhancement can be classified into two types: extension and repair. This paper specifically focuses on the repair type of enhancement. Information systems commonly encounter logging errors or exhibit special behaviors that introduce noise into the event log. In this research, we investigate the process mining model in the presence of noise in the event log. We propose a method for repairing event logs by decomposing them into sub-logs and eliminating the noisy behavior within these sub-logs using covering probability. The repaired sub-logs are then integrated into the original event log at the appropriate location. Additionally, we propose a probabilistic method that considers the frequency of occurrence for activities in a given situation. This method allows for the removal of noisy and abnormal behavior from the event log, providing an overall perspective on the process. To validate our approach, we generate artificial event logs with the presence of noisy behavior using the ProM framework. By using the RapidMiner-based ProM Extension, we generate a test set to illustrate how various types of noisy behavior in an event log can be identified and repaired. Our findings clearly demonstrate that repairing the event log improves the performance of a process mining model.

This paper contributes to the existing literature on variance estimators by utilizing supplementary information. The variance estimation problem of a finite population is a significant matter as sometimes, it is tough to control the variation. For this purpose, an optimum family of exponential variance estimators is suggested under simple random sampling. Moreover, different specific members of the proposed estimators are identified by incorporating various known characteristics of the supplementary variable in the suggested generalized class of estimators. The derivations for the expressions of bias as well as mean square error (MSE) of the proposed estimators are conducted. The suggested family of estimators is studied in different situations by using sets of real data and simulation studies for their performance. To evaluate the efficiency of the suggested estimators, R software is used for the analysis. The study compares the performance of the proposed estimators against the traditional estimators. The theoretical and numerical comparisons show that the estimators suggested in the study are superior in efficiency as compared to the existing estimators.

Recently, several memory-type mean estimators (including ratio, product, and logarithmic) have been developed. These estimators rely on exponentially weighted moving average (EWMA), which incorporate both historical and present sample data. In this article, we propose EWMA type calibrated estimators under single and double stratified random sampling (StRS). Because calibration method enhances the estimates by modifying the stratification weight, taking advantage of supplementary information. To evaluate the performance of estimators, various real-world time-scaled data sets pertaining to stock market and weather are taken into account. Additionally, we also conduct a simulation study using a bivariate symmetric data set. The numerical results show the superiority of proposed estimators (y¯TM,y¯TaM) over the adapted ones (y¯PM,y¯PaM).

Drawing inspiration from recent advancements in robust mean estimation within finite sampling theory, we introduce a novel dual-type class of mean estimators in a design-based framework. The dual-type class is based on quantile regression and is specifically designed to be effective in the presence of extreme observations. Significantly, it integrates the averages of both sampled observations and non-sampled observations of auxiliary variable. In the initial discussion of this class, it is presumed that the target variable is non-sensitive, signifying its relevance to subjects that respondents do not consider embarrassing when queried directly. In this standard setting, we present specific estimators within the class and determine their theoretical properties. The class's scope broadens to include scenarios where the target variable incorporates sensitive topics, giving rise to nonresponse rates and inaccurate reporting. To alleviate these errors, one can promote respondent cooperation by employing scrambled response methods that obscure the actual value of the sensitive variable. Accordingly, the article delves into discussions on additive methods. Subsequently, a numerical study is conducted using asymmetric data to evaluate the effectiveness of the dual-type class by comparing it with several existing estimators, both in the absence and presence of scrambled responses.

In the real-world, there are various situations when all units are not accessible of the respondent called unit non-response. The effect of unit non-response is a tricky matter for estimating the total number of unit. The present work highlights the interest about subpopulations (domains) in two affairs: i. if domains total of the supportive information is accessible ii. if domains total of the supportive variable does not access. The government needs to be introducing the actual facilities in these small domains. The supportive information is used to find out the estimate of the non respondent information and to apply this information for desired domains. Sometimes, it has been found that the accessible auxiliary variable for the domains might be positive shape. Therefore, it develops an appropriate model that has positive skewness. The present context highlighted the indirect method using a power-based estimation with calibration approach. By combining power based estimation and calibration technique, it is possible to obtain more accurate estimates for intended small domains. Even the supportive information is positively biased. This approach helps us in mitigating the effect of non-respondent and improving the overall reliability of the estimators. The simulation was conducted for different sizes 70 and 90 when nonresponse variable in the study variable. The results show that investigated power-based estimate provides better option over relevant exponential, ratio, and generalized regression estimators for intended domains.

The Hotelling T2 statistic is used to compare the mean vectors of two independent multivariate Gaussian distributions. Nevertheless, this statistic is highly sensitive to outliers and is not suitable for high-dimensional datasets where the number of variables exceeds the sample size. This study introduces a robust permutation test based on the minimum regularized covariance determinant (MRCD) estimator to address these limitations of the two-sample Hotelling T2 statistic. Simulation studies were performed to evaluate the proposed test’s empirical size, power, and robustness. Additionally, the test was applied to both uncontaminated and contaminated Alzheimer’s Disease datasets. The findings from the simulations and real data examples provide clues that the proposed test can be effectively used with high-dimensional data without being impacted by outliers. Finally, an R function within the “MVTests” package was developed to implement the proposed test statistic on real-world data.

Abstract Background Immunization is one of the most effective public health initiatives, saving millions of lives and lowering the risk of diseases such as diphtheria, tetanus, influenza, and measles. Immunization saves an estimated 2–3 million lives per year. A study of the regional variations in incomplete immunization will be useful in identifying gaps in the performance of immunization programs that are not noticed by standard vaccination programs monitoring. The primary goal of this study was to identify factors influencing child immunization status and to examine regional variations in incomplete immunization among children aged 12 to 23 months in Pakistan. Methods For the current study, the data were taken from the Demographic and Health Survey for Pakistan (PDHS 2017–2018). Ever-married women who had children aged 12–23 months were included in this study. The immunization status of children was used as an outcome variable. In order to determine the effects of different factors on incomplete immunization, multilevel logistic model was used. To study the geographical variation of incomplete immunization, hotspot analysis was done using ArcGIS 10.7 and SaTScan software and to identify significant predictors of incomplete immunization, GWR 4 software was used. Results Place of delivery, gender of child, mother’s educational level and region were identified as significant determinants of incomplete immunization of children in Pakistan. Chances of incomplete immunization of children were found significantly lower for educated mothers (AOR = 0.52, 95% CI 0.34–0.79) and mothers who had delivered children in the health facilities (AOR = 0.51, 95% CI 0.32–0.83). Female children were more likely (AOR = 1.44, 1.95% CI 1.04–1.99) to be incompletely immunized as compared to male children. FATA (AOR = 11.19, 95% CI 4.89–25.6), and Balochistan (AOR = 10.94, 95% CI 5.08–23.58) were found at the highest risk of incomplete immunization of children as compared to Punjab. The significant spatial heterogeneity of incomplete immunization was found across Pakistan. The spatial distribution of incomplete immunization was clustered all over Pakistan. The high prevalence of incomplete immunization was observed in Balochistan, South Sindh, North Sindh, South KPK, South FATA, Gilgit Baltistan, Azad Jammu Kashmir, South and East Punjab. Drang and Harcho were identified as hotspot areas of incomplete immunization in Gilgit Baltistan. Secondary clusters with a high risk of incomplete immunization were found in regions Balochistan, Sindh and FATA. Conclusion Gender biasedness towards female children, regarding complete immunization of children prevailed in Pakistan. Spatial heterogeneity was also found for incomplete immunization of children. To overcome the problem access to health facilities is the foremost step. Government should target hotspot areas of incomplete immunization of children to provide primary health care facilities by opening health care units in these areas. The government in collaboration with the media should launch awareness campaigns in those areas to convince people that complete immunization is the right of every child regardless of gender.

The present article describes the hydrothermal characteristics of hybrid nanofluid flow over an extending curved Darcy surface. Darcy-Forchheimer effect communicates the nanofluid flow through the permeable surface. The effects of magnetic strength, suction/injection and nonlinear radiation have been also considered. Magnesium-oxide (MgO) and Silver (Ag) nanoparticles (NPs) are dispersed in the base fluid, to produce the hybrid nanofluids (HNF). The modeled equations are numerically computed through the Parametric Continuation Method (PCM). The upshot of flow constraints on the energy, mass and velocity contour is graphically presented and explained. The result shows that when the curvature component is taken into account, the energy is lowered, but the velocity curve is elevated. The consequences of thermal Biot number intensify the heat transportation rate. By raising the amount of nanoparticle in the base fluid, energy and velocity profiles are enhances. It has been detected that the energy transmission rate improves up to 27.3% by using nanofluid (MgO-water) as the range of volume friction parameter rises from 0.02 to 0.04. However, 39.97% enhancement is observed in the energy transmission rate between nanoliquid and hybrid nanofluid (Ag–MgO/water) as the range of volume friction parameter rises from 0.01 to 0.04.

This paper shows the stagnant point flow of Powell-Eyring hybrid nanofluids due to a stretching sheet. The Xue and Yamada-Ota based on hybrid nanoliquid have been subjected to a comparison study that has been scrutinized. The suspension of two nanoparticles AA 7072 and AA 7075 with base fluid Ethylene glycol ( EG ) is studied through hybrid nanoliquid. With the implementation of the noteworthy suitable alteration, the system of equations in terms of ODEs is established. The bvp4c technique is then applied to obtain the numerical solution of reduced ODEs. The significance of physical quantities over thermal, velocity, force friction, and heat transport are elaborated in tabular form and also in graphical form. During this analysis, the Xue model produced less heat transport as compared to the Yamada-Ota hybrid nanofluid. The result shows that the Xue model produces less heat gradient equated to the Yamada-Ota model. The velocity profile is enhanced and the thermal profile has decayed with the larger value of the fluid parameter.

This paper focuses on the applications of Landmark method for obtaining dynamic predictions of survival by using Landmark approach to the data of asthma prevention trial in young children. This work focuses on the different ways to model recurrent events by considering various time scales according to how subjects in the dataset experienced multiple events. Landmark models can be used to dynamically estimate the effect of treatments effects whilst also taken into consideration the history of previous asthma attacks. Our analysis show that the treatment effect should be modelled with a time varying effect and the effect of the previous attack reduces with the passage of time.

Outliers are observations that are significantly different from the other observations in a dataset. These types of observations are asymmetric in nature due to a lack of symmetry. The estimation of the cumulative distribution function (CDF) is an important statistical measure commonly discussed for symmetric datasets. However, the estimation of the CDF in the case of the asymmetric nature of the dataset is not a much-explored topic. In this article, we use calibration methodology with auxiliary information for modifying the traditional stratification weight, and hence, we obtain efficient estimates of the CDF using robust measures, i.e., mid-range and tri-mean, under the different distance functions. A simulation study is carried out to see the performance of proposed and existing estimators using asymmetric real-life datasets.

Using auxiliary information, the calibration approach modifies the original design weights to enhance the mean estimates. This paper initially proposes two families of estimators based on an adaptation of the estimators presented by recent researchers, and then, it presents a new family of calibration estimators with the set of some calibration constraints under stratified median ranked set sampling (MRSS). The result has also been implemented to the situation of two-stage stratified median ranked set sampling (MRSS). To best of our knowledge, we are presenting for the first time calibration-based mean estimators under stratified MRSS, so the performance evaluation is made between adapted and proposed estimators on behalf of the simulation study with real and artificial datasets. For real-world data or applications, we use information on the body mass index (BMI) of 800 people in Turkey in 2014 as a research variable and age as an auxiliary variable.

Surprising perceptions may happen in survey sampling. The arithmetic mean estimator is touchy to extremely enormous or potentially small observations, whenever selected in a sample. It can give one-sided (biased) results and eventually, enticed to erase from the selected sample. These extremely enormous or potentially small observations, whenever known, can be held in the sample and utilized as supplementary information to expand the exactness of estimates. Also, a supplementary variable is consistently a well-spring of progress in the exactness of estimates. A suitable conversion/transformation can be utilized for getting much more precise estimates. In the current study, regarding population mean, we proposed a robust class of separate type quantile regression estimators under stratified random sampling design. The proposed class is based on extremely enormous or potentially small observations and robust regression tools, under the framework of Särndal. The class is at first defined for the situation when the nature of the study variable is nonsensitive, implying that it bargains with subjects that do not create humiliation when respondents are straightforwardly interrogated regarding them. Further, the class is stretched out to the situation when the study variable has a sensitive nature or theme. Sensitive and stigmatizing themes are hard to explore by utilizing standard information assortment procedures since respondents are commonly hesitant to discharge data concerning their own circle. The issues of a population related to these themes (for example homeless and nonregular workers, heavy drinkers, assault and rape unfortunate casualties, and drug users) contain estimation errors ascribable to nonresponses as well as untruthful revealing. These issues might be diminished by upgrading respondent participation by scrambled response devices/techniques that cover the genuine value of the sensitive variable. Thus, three techniques (namely additive, mixed, and Bar-Lev) are incorporated for the purposes of the article. The productivity of the proposed class is also assessed in light of real-life dataset. Lastly, a simulation study is also done to determine the performance of estimators.