The aim of this work is to develop a new outstanding lifetime distribution, dubbed the power Bilal (PB) distribution. Both of the probability distribution function (pdf) and the cumlative distribution function (cdf) of the PB distribution have a simple forms. The suggested distribution’s moments, incomplete moments as well as the quantile function are deduced and acquired in explicit forms as a result of its simple forms. Seven estimation methods for estimating the PB distribution parameters are mentioned, and numerical simulations are used to compare the proposed approaches using partial and overall ranks. According to the simulation results of this work, the maximum likelihood estimators are advised to be the best estimation method for estimating the parameters of the PB distribution, when the data genrated from the PB distribution. We shows the importance and flexibility of the PB distribution by comparing it to other existing competing distributions using two different real data sets from COVID-19 mortality rates of two countries.

The objective of this article is to conduct a full study on the failure times of items when subjected to a progressive-stress accelerated life test. These failure times follow the Modified Kies exponential distribution. We performed the experiments under a type-II censoring scheme with binomial removal. The stress design has two ways to be applied either the simple ramp-stress test or the multiple ramp-stress level design of acceleration. We made a comparison between these two designs to decide which design is better. When the lifetime of test units follows the Modified Kies distributions, the cumulative exposure model has been used to apply the acceleration on the failure times to produce early failures. The simulation study was done to compare two types of progressive-stress designs. Different estimation techniques such as maximum likelihood estimation and Bayes estimation are employed to estimate the model parameters. The Metropolis Hasting method is used to derive the Bayesian estimates under symmetric and asymmetric loss functions. We also developed interval estimation as well as point estimation, and we estimated the asymptotic confidence intervals, bootstrap, and credible for the distribution parameters. We made a comparison between different estimation methods. We used real data from a practical experiment as a real data set example to assess the performance of the estimations methods. These data are analyzed to demonstrate the adequacy and superiority of the distribution to fit accelerated failure times. Also, we studied the existence and uniqueness of the roots and we used graphs to assure that the estimates used are unique and global maximum. Finally, some noteworthy conclusions are reached.

In this paper, we developed a novel superior distribution, demonstrated and derived its mathematical features, and assessed its fuzzy reliability function. The novel distribution has numerous advantages, including the fact that its CDf and PDf have a closed shape, making it particularly relevant in many domains of data science. We used both conventional and Bayesian approaches to make various sorts of estimations. A simulation research was carried out to investigate the performance of the classical and Bayesian estimators. Finally, we fitted a COVID‐19 mortality real data set to the suggested distribution in order to compare its efficiency to that of its rivals.

This paper introduces a novel generalization of the Ailamujia distribution. We introduce a skewness parameter to the Ailamujia distribution and rename it the new weighted Ailamujia distribution. We introduce some statistical properties of the new weighted Ailamujia distribution and present some important results on the effect of the skewness parameter on the density of distribution. We estimate the parameters of the new weighted Ailamujia distribution by using the maximum likelihood technique and apply the proposed distribution to model a real dataset. Received: July 1, 2023 Revised: August 30, 2023 Accepted: September 15, 2023

In this research, we studied the mixture of normal and half-normal distributions and introduced some properties for this mixture. In particular, we derived the mean, median, and mode of the mixture of normal and half-normal distributions. We also focused on exploring the Bayesian estimation of parameters of the mixture of normal and half-normal distributions by using different methods and then, using type-I censored sample units, presented a simulation study on the mixture of normal and half-normal distributions.