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Two-stage cluster sampling is often employed in survey sampling when complete population information is not available. In this setting, the Exponentially Weighted Moving Average (EWMA) statistic offers an efficient way to estimate the population mean by incorporating both past and current data. Motivated by this, we propose a class of memory-type ratio and exponential estimators for estimating the population mean under a two-stage cluster sampling framework. Theoretical expressions for the biases and mean square errors (MSE) of the proposed estimators are derived. To evaluate their performance, a comprehensive simulation study was carried out, supplemented by an empirical application. Several special cases of the proposed estimators were also considered and compared with existing two-stage estimators. The analysis was performed under different values of the EWMA smoothing constant ( λ = 0 . 3 , 0 . 5 , 0 . 75 , 0 . 9 ). Both simulation and empirical results consistently show that the proposed memory-type two-stage ratio estimators outperform existing approaches, providing improved efficiency with minimum MSE.

Calibration methods play a vital role in improving the accuracy of parameter estimates by effectively integrating information from various data sources. In the context of population parameter estimation, memory-type statistics—such as the exponentially weighted moving average (EWMA), extended exponentially weighted moving average (EEWMA), and hybrid exponentially weighted moving average (HEWMA)—leverage both current and historical data. This study proposes new ratio and product estimators within a calibration framework that utilizes these memory-type statistics. A simulation study is conducted to evaluate the performance of the proposed estimators. The mean squared error (MSE) and relative efficiency (RE) are computed, accompanied by graphical representations to illustrate the behavior of the estimators. The performance of the proposed estimators is compared with existing memory-type estimators. Furthermore, a real-world application is presented to validate the effectiveness of the proposed methods. The comparison, based on MSE and RE across different values of the smoothing constant, demonstrates that the calibration-based memory-type estimators outperform the existing approaches. The results indicate that the proposed estimators consistently achieve lower MSE and higher RE, confirming their superiority over traditional methods.

In survey statistics, estimating and reducing population variation is crucial. These variations can occur in any sampling design, including stratified random sampling, where stratum weights may increase the variance of estimators. Calibration techniques, which use additional auxiliary information, can help mitigate this issue. This paper examines three calibration-based estimators—calibration variance, calibration ratio, and calibration exponential ratio estimators—within the framework of stratified random sampling. The study generates data from normal, gamma, and exponential distributions to test these estimators. Results demonstrate that the proposed calibration estimators offer more accurate estimates of population variance and outperform existing methods in estimating population variance under stratified random sampling, providing more accurate and reliable estimates.

Survey sampling is a widely used technique for collecting data from a subset of a bigger population. Among its methods, stratified random sampling is particularly valuable for yielding precise inferences about distinct subgroups within a population by dividing the population into mutually exclusive strata and sampling from each group. This approach reduces sampling error and enhances the accuracy of population estimates. In this study, we propose a set of improved calibrated log-ratio-type estimators for estimating population variance under a stratified sampling framework. The performance of three proposed estimators is evaluated and compared in terms of the mean squared error. A simulation study is conducted to assess the efficiency of the estimators, complemented by a real-life application to validate the simulation results. The findings demonstrate that the proposed calibrated log-ratio variance estimators outperform existing methods by achieving lower mean squared error.

Statistical process control basically involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. It is used extensively in the field of reliability engineering. The reliability of the production process is thoroughly monitored for any internal variation using the SPC. The aim is always to settle such variations through a proper control monitoring. If the underlying distribution of the process is known to the researcher than the use of parametric control charts are useful but in many cases when there is doubt about the distribution of the process then it is preferred to use non parametric control charts. In this paper we propose the modified Exponentially weighted moving average (EWMA), Double Exponentially weighted moving average (DEWMA), Hybrid Exponentially weighted moving average (HEWMA), Extended Exponentially weighted moving average (EEWMA), Modified Exponentially weighted moving average (MEWMA) and mix- type control charts by mixing these control charts with Tukey control chart EWMA-TCC, DEWMA-TCC, HEWMA-TCC, EEWMA-TCC, MEWMA-TCC for the shape parameter of the Kumaraswamy Lehmann-2 Power function distribution (KL2PFD).

We explore the cosmic evolution of the accelerating universe in the framework of dynamical Chern–Simons modified gravity in an interacting scenario by taking the flat homogeneous and isotropic model. For this purpose, we take some parametrizations of the equation of state parameter. This parametrization may be a Taylor series extension in the redshift, a Taylor series extension in the scale factor or any other general parametrization of ω . We analyze the interaction term which calculates the action of interaction between dark matter and dark energy. We explore various cosmological parameters such as deceleration parameter, squared speed of sound, Om-diagnostic and statefinder via graphical behavior.

This article introduces a new probability model based on reflected parameter called the reflected Pareto (RP) distribution. The key properties of the RP model are investigated. A simulation study of the RP model is conducted to evaluate the performances of its estimators. A real-life application is considered to examine the performance of proposed model. The different criteria are discussed numerically as well as graphically to show the flexibility of the RP model. The exponential weighted moving average control charts based on the maximum likelihood and modified maximum likelihood estimators for the shape parameter of the RP distribution are obtained. Detailed simulation results of proposed charts are performed to examine and analyze the performance of these charts with three in-control average run length values and two sample sizes. Finally, the application of the proposed control charts is shown by considering a real-life data set.

Background Statistical process control (SPC) is utiled in manufacturing and service applications. It is used to monitor the behavior of the process, also to discover and solve the issues in internal systems. SPC allows immediate corrective actions to prevent defects and maintain process stability. There are two types of control charts are available in the literature: variable control charts and attribute control charts. Methods The use of attribute control charts for two positively skewed distributions such as power function distribution and weighted power function distribution is discussed in this research paper. We compared the behavior of both types of control charts and presented the results in form of tables. Results We conclude that control charts under a weighted power function distribution perform better than control charts using a power function distribution. Furthermore, these results will help in the early detection of errors that enhance the process reliability of the telecommunications and financing industries.

Objectives: To assess the functional health literacy among adolescents of Model schools of Islamabad. To determine association between health literacy and health seeking behaviour of adolescents.Study Design: Cross sectional descriptive study.Place and duration of study: The study was conducted in Model schools of Islamabad, from Jan to Dec 2016.Material and Methods: Multi stage systematic sampling was done and a sample size of 350 using WHO sample size calculator. After taking informed consent from the students data were collected using the newest vital sign (NVS) for assessment of functional health literacy. Data were analyzed using SPSS version 22.Results: The mean age of the respondents was 15 (SD ± 0.6) years. There were 181 (52%) females and 169 (48%) males in the study. Out of 350 respondents 73 (20.9%) had very limited health literacy, while 187 (53.4%) had limited while 90 (25.7%) had adequate health literacy. In health seeking 30 students (8.6%) scored 1-2 on the health seeking behaviour score of 1-6 and therefore were categorized as having poor health seeking behaviour. While 164 students (46.9%) scored 3-4 and were categorized as having satisfactory health seeking. One hundred and fifty six students (44.6%) scored 4-5 and had good health seeking behaviour.Conclusion: The health literacy among the adolescents was limited and had no association with health seeking behaviour.