A new extension of XLindley distribution with mathematical properties, estimation, and application on the rainfall data.

Data analysis is indeed quite popular and crucial in various fields such as meteorology, hydrology, epidemiology, economics, and biology. So, the purpose of this study is to introduce a new probability distribution to analyze rainfall data. A new extension of XLindley distribution is introduced using the alpha power transformation technique. The new distribution is named "alpha power transformed XLindley - (APTXL) distribution". Mathematical properties of APTXL distribution are derived such as ordinary moments, moment generating function, quantile function, mean residual life function, and order statistics. The model parameters are estimated using five different estimation methods such as maximum likelihood, Anderson Darling, Cramer von Misses, Ordinary least squares, and weighted least squares. A comprehensive simulation study is utilized to check the behavior and efficiency of the derived estimators. It is found that the weighted least square approach efficiently estimates the model parameter than the other methods. This derivation of a new model not only contributes to theoretical advances in statistical methodology but also provides practical methods for rainfall data modeling. The APTXL distribution is used to evaluate rainfall datasets from Saudi Arabia. It is identified that the APTXL distribution provides efficient results as compared to considered competitive distributions.

A new class of Lindley distribution: System reliability, simulation and applications.

This paper presents a new probability distribution called the DUS Lindley distribution, created by applying the DUS transformation to the traditional Lindley distribution. The study provides an in-depth analysis of the distribution's statistical properties. These properties include a variety of statistical measures such as the probability density function, cumulative distribution function, failure rate, survival function, reverse hazard function, Mills ratio, mean residual life, mean past life, moments, conditional moments, characteristic function, order statistics, entropy measures, likelihood ratio test and Lorenz and Bonferroni curves. Parameter estimation is performed using several methods including weighted least squares, maximum likelihood estimation, Cramer-Von Mises estimation, least squares and Anderson-Darling estimation. The paper also explores the estimation of system reliability and evaluates the performance of maximum likelihood estimators through simulation studies across different sample sizes. Finally, the DUS Lindley distribution is applied to two real-world datasets, demonstrating a better fit than other well-known distributions.

Estimation methods based on ranked set sampling for the power logarithmic distribution.

The sample strategy employed in statistical parameter estimation issues has a major impact on the accuracy of the parameter estimates. Ranked set sampling (RSS) is a highly helpful technique for gathering data when it is difficult or impossible to quantify the units in a population. A bounded power logarithmic distribution (PLD) has been proposed recently, and it may be used to describe many real-world bounded data sets. In the current work, the three parameters of the PLD are estimated using the RSS technique. A number of conventional estimators using maximum likelihood, minimum spacing absolute log-distance, minimum spacing square distance, Anderson-Darling, minimum spacing absolute distance, maximum product of spacings, least squares, Cramer-von-Mises, minimum spacing square log distance, and minimum spacing Linex distance are investigated. The different estimates via RSS are compared with their simple random sampling (SRS) counterparts. We found that the maximum product spacing estimate appears to be the best option based on our simulation results for the SRS and RSS data sets. Estimates generated from SRS data sets are less efficient than those derived from RSS data sets. The usefulness of the RSS estimators is also investigated by means of a real data example.

The development of an extended Weibull model with applications to medicine, industry and actuarial sciences.

This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.

Group acceptance sampling plan based on truncated life tests for Type-I heavy-tailed Rayleigh distribution.

This study on the Type-I heavy-tailed Rayleigh (TI-HTR) distribution is a special case of Type-I heavy-tailed (TI-HT) family of distributions was studied. The characteristics were derived, including the moment and its measures, quantile function, reliability measures, and other statistical properties as well as parameter estimation using the maximum likelihood method and penalized likelihood estimation. The behavior of its various functions were shown graphically. Analytically, we showed that model linearly grows near the origin and exhibits rapid exponential decay. However, the tail behavior cannot equal the traditional heavy-tail in the power law sense, hence it is called the type-I heavy-tail. Interestingly, we designed a group acceptance plan (GASP) and demonstrated usefulness with both assumed and maximum likelihood estimates. The GASP under the TI-HTR distribution is preferable when the parameter values are small. The distribution was used to model real-life data sets to justify its usefulness. The results of the application of the model to both COVID-19 and Cancer data showed that the model fits the two data better than the competing models and also suggest that inference from the model is better than those of the competitors. In estimating the parameters, the penalized likelihood procedure perform considerably better with minimum standard error of the estimates. From the Cramér-von Mises test results which guides against the heavy-tail sensitivity, the TI-HTR distribution offers a better model for fitting fast decaying exponential data since it has the least statistics in both datasets.

A novel weighted family of probability distributions with applications to world natural gas, oil, and gold reserves.

Recent innovations have focused on the creation of new families that extend well-known distributions while providing a huge amount of practical flexibility for data modeling. Weighted distributions offer an effective approach for addressing model building and data interpretation problems. The main objective of this work is to provide a novel family based on a weighted generator called the length-biased truncated Lomax-generated (LBTLo-G) family. Discussions are held about the characteristics of the LBTLo-G family, including expressions for the probability density function, moments, and incomplete moments. In addition, different measures of uncertainty are determined. We provide four new sub-distributions and investigated their functionalities. Subsequently, a statistical analysis is given. The LBTLo-G family's parameter estimation is carried out using the maximum likelihood technique on the basis of full and censored samples. Simulation research is conducted to determine the parameters of the LBTLo Weibull (LBTLoW) distribution. Four genuine data sets are considered to illustrate the fitting behavior of the LBTLoW distribution. In each case, the application outcomes demonstrate that the LBTLoW distribution can, in fact, fit the data more accurately than other rival distributions.

A novel proposed class of estimators under ranked set sampling: Simulation and diverse applications.

This study presents a novel enhanced exponential class of estimators for population mean under RSS by employing data on an auxiliary variable. The suggested estimators' mean square error (MSE) is calculated approximately at order one. The efficiency conditions that make the suggested enhanced exponential class of estimators superior to the traditional estimators are found. A simulation study using hypothetically drawn normal and exponential populations evaluates the execution of the suggested estimators. The findings demonstrate that the suggested estimators outperform their traditional equivalents. In addition, real data examples are examined to show how the proposed estimators can be implemented in various real life problems.

An enhanced estimator of finite population variance using two auxiliary variables under simple random sampling.

In this article, we have suggested a new improved estimator for estimation of finite population variance under simple random sampling. We use two auxiliary variables to improve the efficiency of estimator. The numerical expressions for the bias and mean square error are derived up to the first order approximation. To evaluate the efficiency of the new estimator, we conduct a numerical study using four real data sets and a simulation study. The result shows that the suggested estimator has a minimum mean square error and higher percentage relative efficiency as compared to all the existing estimators. These findings demonstrate the significance of our suggested estimator and highlight its potential applications in various fields. Theoretical and numerical analyses show that our suggested estimator outperforms all existing estimators in terms of efficiency. This demonstrates the practical value of incorporating auxiliary variables into the estimation process and the potential for future research in this area.