Here, we present a new bounded distribution known as the power Lambert uniform distribution, and we deduce some of its statistical properties such as quantile function, moments, incomplete moments, mean residual life and mean inactivity time, Lorenz, Bonferroni, and Zenga curves, and order statistics. We presented different shapes of the probability density function and the hazard function of the proposed model. Eleven traditional methods are used to estimate its parameters. The behavior of these estimators is investigated using simulation results. Some actuarial measures are derived mathematically for our proposed model. Some numerical computations for these actuarial measures are given for some choices of parameters and significance levels. A new quantile regression model is constructed based on the new unit distribution. The maximum likelihood estimation method is used to estimate the unknown parameters of the regression model. Furthermore, the usability of the new distribution and regression models is demonstrated with the COVID-19 and educational datasets, respectively.

This work proposes a new extension to the XLindley model called an inverse XLindley distribution (IXLD). Its probability density function and hazard rate function shapes were deduced mathematically. Several statistical properties of the IXLD were derived mathematically. We use ten different approaches to calculate the parameters of the IXLD. The asymptotic behaviour of these estimators were studied thanks to a comprehensive simulation investigation. Through modelling real data sets, the effectiveness and applicability of the IXLD are examined. This proves that the IXLD better fits the real data set than competing models.

This research article introduces a new family of distributions developed using the innovative beta-generated transformation technique. Among these distributions, the focus is on the inverse exponential power distribution, which exhibits unique reverse-J, inverted bathtub, or monotonically increasing hazard functions. This paper thoroughly investigates the distribution’s key characteristics and utilizes the maximum likelihood estimation method to determine its associated parameters. To assess the accuracy of the estimation procedure, the researchers conducted a simulation experiment, revealing diminishing biases and mean square errors with increasing sample sizes, even when working with small samples. Moreover, the practical applicability of the proposed distribution is demonstrated by analyzing real-world COVID-19 and medical datasets. The article establishes that the proposed model outperforms existing models by using model selection criteria and conducting goodness-of-fit test statistics. The potential applications of this research extend to various fields where modeling and analyzing hazard functions or survival data are crucial. Additionally, the study contributes to advancing probability theory and statistical inferences.

This paper introduces the power new XLindley (PNXL) distribution, a novel two-parameter distribution derived using the power transformation method applied to the XLindley distribution. We thoroughly explore the structural properties of the PNXL distribution, including the rth moment about the origin, moment generating function, survival rate function, distribution function, hazard rate function, skewness, kurtosis, and coefficient of variation. Additionally, we derive the quantile function, fuzzy reliability, reliability measures, stochastic ordering, and actuarial measures for this new distribution. To estimate the parameters of the PNXL distribution, we propose several estimators and evaluate their performance through extensive simulation studies. To demonstrate the applicability and superiority of the PNXL distribution over existing distributions, we fit it to two real datasets and compare its performance with potential competing models. The results highlight the PNXL distribution's effectiveness and potential as a robust tool for modeling and analyzing real-world data.

This article introduces a new statistical distribution called the power unit Burr-XII distribution, which is an extension of the Burr XII distribution obtained through a power transform. This paper investigates several statistical properties of this new model, including mode, moments, moment generating and characteristic functions, entropy, and Bonferroni and Lorenz curves. In addition, various classical estimators for the parameters of the power unit Burr-XII distribution are evaluated, including maximum likelihood estimates, ordinary least squares estimates, maximum product of interval estimates, Anderson–Darling, right and left tail Anderson–Darling, and Cramer–von Mises estimators. This study provides tables and graphs to illustrate the performance of these methods under different scenarios and sample sizes. The results of the proposed distribution in different fields of application are shown using the mortality rates of COVID-19 patients in Spain and flood data from 20 observations. As a result of both applications, it was observed that the proposed distribution gave better results compared to other well-known distributions, such as the beta distribution, transformed gamma distribution, log-weighted power distribution, transmuted power distribution, Kumaraswamy distribution, Topp–Leone distribution, exponentiated reduce Kies distribution, and exponentiated Topp–Leone distribution.