Improved estimation of population distribution function using twofold auxiliary information under simple random sampling.

In this article, our main aim is to suggest enhanced families of estimators for estimating the population distribution function (DF) using twofold auxiliary evidence within the framework of simple random sampling. Numerical analysis is performed on four different actual data sets. The precision of the estimators is further investigated exhausting a simulation study. As equated with existing estimators, the suggested families of estimators have minimum mean square error (MSE) and higher percentage relative efficiency (PRE). The succeeding recommended family of estimators outperforms the first family of estimators across all data sets. These are positive indicators of its performance. The theoretical result shows that the recommended family of estimators performs better than the existing estimators. The extent of improvement in efficiency is noteworthy, indicating the superiority of the suggested estimators in terms of minimum MSE.

A new approach for estimating variance of a population employing information obtained from a stratified random sampling.

In this article, we suggest an enhanced estimator for the estimation of finite population variance using twofold auxiliary variable under stratified random sampling. The numerical expressions for the bias and MSE are determined up to the first order of approximation. In order to effectively validate the theoretical findings, three actual data sets are included. Additionally, the application of the suggested estimators is demonstrated using a simulation study. Results of an empirical comparison among the suggested and existing estimators were investigated. To determine how good the suggested estimator, in comparison to the preliminary estimators, the MSE criterion is used. The suggested estimator has a smaller MSE and better PRE than existing estimators, according to numerical results utilizing actual data sets and a simulation analysis.

Efficient estimation of population variance of a sensitive variable using a new scrambling response model.

This study introduces a pioneering scrambling response model tailored for handling sensitive variables. Subsequently, a generalized estimator for variance estimation, relying on two auxiliary information sources, is developed following this novel model. Analytical expressions for bias, mean square error, and minimum mean square error are meticulously derived up to the first order of approximation, shedding light on the estimator's statistical performance. Comprehensive simulation experiments and empirical analysis unveil compelling results. The proposed generalized estimator, operating under both scrambling response models, consistently exhibits minimal mean square error, surpassing existing estimation techniques. Furthermore, this study evaluates the level of privacy protection afforded to respondents using this model, employing a robust framework of simulations and empirical studies.

Enhancing mean estimators in median ranked set sampling with dual auxiliary information.

When measuring the research variable is complicated, expensive, or problematic, median ranked set sampling (MRSS) is often utilized since it is straightforward to rank the components using a low-cost sorting criterion. Using this sampling scheme, many authors considered the problem of population mean estimation with a single auxiliary variable in order to obtain more precised estimators than the traditional ratio type regression estimators. In this article, we extend their ideas based on regression approach using two auxiliary variables and introduce a new regression-type estimator along with its theoretical expression of minimum mean square error (MSE). The suggested estimator's applicability is demonstrated using both simulated and real-world data sets.

A new alpha logarithmic-generated class to model precipitation data with theory and inference.

Precipitation, or rainfall, is a central feature of the weather cycle and plays a vital role in sustaining life on Earth. However, existing models such as the Poisson, exponential, normal, log-normal, generalized Pareto, gamma, generalized extreme value, lognormal, beta, Gumbel, Weibull, and Pearson type III distributions used for predicting precipitation are often inadequate for precisely representing the complex pattern of rainfall. This study proposes a novel and innovative approach to address these limitations through the new alpha logarithmic-generated (NAL-G) class of distributions. The study authors thoroughly examine the NAL-G class and a unique model, the NAL-Exponential (NAL-Exp) distribution, with a focus on analyzing mathematical properties such as moments, quantile function, entropy, order statistics, and more. Six recognized classical estimation methods are employed, and extensive simulations are conducted to determine the best one. The NAL-Exp distribution demonstrates its high adaptability and value through its superior performance in modeling four distinct rainfall data sets. The results show that the NAL-Exp distribution outperforms other commonly used distribution models, highlighting its potential as a valuable tool in hydrological modeling and analysis. The increased versatility and flexibility of this new approach hold great potential for enhancing the accuracy and reliability of future rainfall predictions.

Statistical inferences under step stress partially accelerated life testing based on multiple censoring approaches using simulated and real-life engineering data.

Evaluating the lifespan distribution of highly reliable commodities under regular use is exceedingly difficult, time consuming, and extremely expensive. As a result of its ability to provide more failure data faster and at a lower experimental cost, accelerated life testing has become increasingly important in life testing studies. In this article, we concentrate on parametric inference for step stress partially life testing utilizing multiple censored data based on the Tampered Random Variable model. Under normal stress circumstances, the lifespan of the experimental units is assumed to follow the Nadarajah-Haghighi distribution, with and being the shape and scale parameters, respectively. Maximum likelihood estimates for model parameters and acceleration factor are developed using multiple censored data. We build asymptotic confidence intervals for the unknown parameters using the observed Fisher information matrix. To demonstrate the applicability of the different methodologies, an actual data set based on the timings of subsequent failures of consecutive air conditioning system failures for each member of a Boeing 720 jet aircraft fleet is investigated. Finally, thorough simulation studies utilizing various censoring strategies are performed to evaluate the estimate procedure performance. Several sample sizes were studied in order to investigate the finite sample features of the considered estimators. According to our numerical findings, the values of mean squared errors and average asymptotic confidence intervals lengths drop as sample size increases. Furthermore, when the censoring level is reduced, the considered estimates of the parameters approach their genuine values.