To estimate the finite population variance of the study variable, this paper proposes an improved class of efficient estimators using different transformations. When both the minimum and maximum values of the auxiliary variable are known and the ranks of the auxiliary variable are associated with the study variable, these estimators are particularly useful. Therefore, the precision of the estimators can be effectively improved through the utilization of these rankings. We examine the properties of the proposed class of estimators, including bias and mean squared error (MSE), using a first-order approximation through a stratified random sampling method. To determine the performances and validate the findings mathematically, a simulation study is carried out. Based on the results, the proposed class of estimators performs better in terms of the mean squared error $\left(MSE\right)$ and percent relative efficiency $\left(PRE\right)$ as compared to other estimators in all scenarios. Furthermore, in order to prove that the performances of the improved class of estimators are better than those of the existing estimators, three data sets are examined in the application section.

Statistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the mixed state, the utilization of the traditional probability models is not a suitable choice. Therefore, searching for more flexible probability models that are capable of adequately describing the mixed state failure data sets is an interesting research topic for researchers. In this paper, we propose and study a new statistical model to achieve the above goal. The proposed model is called a new beta power very flexible Weibull distribution and is capable of capturing five different patterns of the failure rate such as uni-modal, decreasing-increasing-decreasing, bathtub, decreasing, increasing-decreasing-increasing shapes. The estimators of the new beta power very flexible Weibull distribution are obtained using the maximum likelihood method. The evaluation of the estimators is assessed by conducting a simulation study. Finally, the usefulness and applicability of the new beta power very flexible Weibull distribution are shown by analyzing two engineering data sets. Using four information criteria, it is observed that the new beta power very flexible Weibull distribution is the best-suited model for dealing with failure times data sets.

This article presents a new set of estimators designed to estimate the finite population variance of a study variable in two-phase sampling. These estimators utilize the information about extreme values and ranks of an auxiliary variable. Through a first-order approximation, we investigate the properties of these estimators, including biases and mean squared errors (MSEs). Furthermore, a comprehensive simulation study is conducted to assess their performance and validate our theoretical insights. Results demonstrate that our proposed class of estimators performs better in terms of percent relative efficiency (PRE) across various simulation scenarios compared to existing estimators. In addition, in the application section, we utilize three data sets to further validate the performance of our proposed estimators against conventional unbiased variance estimators, ratio and regression estimators, as well as other existing methods.

This article suggests an improved class of efficient estimators that use various transformations to estimate the finite population variance of the study variable. These estimators are particularly helpful in situations where we know about the minimum and maximum values of the auxiliary variable, and the ranks of the auxiliary variable are associated with the study variable. Consequently, these rankings can be applied as an effective tool to improve the accuracy of the estimator. A first-order approximation is used to investigate the properties of the proposed class of estimators, such as bias and mean squared error ($MSE$) under simple random sampling. A simulation study carried out in order to measure the performance and verify the theoretical results. The suggested class of estimators has a greater percent relative efficiency ($PRE$) than the other existing estimators in all of the simulated situations, according to the results. Three symmetric and asymmetric datasets are examined in the application section in order to show the superior performance of the proposed class of estimators over the existing estimators.

Smarandache developed the idea of hypersoft set (HSS) theory as an extension of soft set (SS) theory. HSS provides a general mathematical framework for handling data that can be formulated as several trait-valued disjoint sets which blend to various traits. The major goal of this article is to lay the footing for supplying a new model called bipolar fuzzy hypersoft sets (BFHSSs) by linking both fuzzy sets (FSs) and HSSs under bipolarity property. By using positive and negative membership functions and multi-argument functions, these structures work best for testing uncertainty. This makes them better at solving real-world problems, especially ones that have both good and bad sides. This paper also has different operations for BFHSSs, such as absolute BFHSS, null BFHSS, complement, subset, union, intersection, and their related properties. Moreover, operations like OR and AND for BFHSS have been instituted. Some properties are demonstrated, and some numerical examples are given to illustrate the mechanism of using these tools. Finally, these tools are applied in the decision-making process based on an algorithm that is built.

Survey sampling commonly faces the challenge of missing information, prompting the development of various imputation-based mean estimation methods to address this concern. Among these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent pioneering research has revolutionized this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This groundbreaking methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present novel imputation-based memory-type mean estimators that leverage EWMA and quantile regression to handle missing observations. For the performance assessment between traditional, adapted and proposed estimators, real-life time-scaled datasets related to the stock market and humidity are considered. Furthermore, we conduct a simulation study using an asymmetric dataset to further validate the effectiveness of the introduced estimators. The humidity data results show that the proposed estimators ($T_{p_{q_{\left(0.25\right)}}}$, $T_{p_{q_{\left(0.45\right)}}}$, $T_{p_{q_{\left(0.25\right)}}}^{{}^{\prime }}$, $T_{p_{q_{\left(0.45\right)}}}^{{}^{\prime }}$, $T_{p_{q_{\left(0.25\right)}}}^{{}^{″}}$, $T_{p_{q_{\left(0.45\right)}}}^{{}^{″}}$) have the minimum MSE. The stock market data results show that the proposed estimators ($T_{p_{q_{\left(0.85\right)}}}$, $T_{p_{q_{\left(0.85\right)}}}^{{}^{\prime }}$, $T_{p_{q_{\left(0.85\right)}}}^{{}^{″}}$) also have the minimum MSE. Additionally, the simulation results demonstrate that the proposed estimators ($T_{p_{q_{\left(0.45\right)}}}$, $T_{p_{q_{\left(0.45\right)}}}^{{}^{\prime }}$, $T_{p_{q_{\left(0.45\right)}}}^{{}^{″}}$) have the minimum MSE when compared to traditional and adapted estimators. Therefore, in conclusion, the use of the proposed estimators is recommended over traditional and adapted ones.