The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp–Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp–Leone (TPITL) distribution. The power inverted Topp–Leone and the inverted Topp–Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp–Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

This work will address the problem of estimating the parameters for the Nadaraj ah–Haghighi (NH) distribution using progressive Type-1 censoring (PT1C) utilizing Bayesian and non-Bayesian approaches. To apply PT1C, censoring times for each stage of censoring needed to be known before the experiment started. To solve this issue of censoring time selection, qauntiles from the NH lifetime distribution will be used as PT1C censoring time points. Maximum likelihood (ML) estimators (MLEs) and asymptotic confidence intervals (ACoIs) are produced with a focus on the censoring technique. Bayes estimates (BEs) and accompanying maximum posterior density (PD) credible interval estimations are also created via the squared error (SEr) loss function. The BEs are evaluated using the Markov Chain Monte Carlo (MCMC) technique and the Metropolis–Hasting (MH) algorithm. An analysis of an actual data set demonstrates the theoretical implications of MLEs and BEs for defined schemes of PT1C samples. Finally, simulation results will be used to compare the performance of the various recommended estimators.

A novel lifetime distribution has been defined and examined in this study. The odd Lindley–Pareto (OLiP) distribution is the name we give to the new distribution. The new density function can be written as an odd Lindley-G distribution with Pareto amplification. The moment-generating function and characteristic function, entropy and asymptotic behavior, order statistics and moments, mode, variance, skewness, and kurtosis are some of the aspects of the OLiP distribution that are discovered. Seven non-Bayesian estimation techniques and Bayesian estimation utilizing Markov chain Monte Carlo were compared for performance. Additionally, when the lifetime test is truncated after a predetermined period, single acceptance sampling plans (SASPs) are created for the newly suggested, OLiP distribution. The median lifetime of the OLiP distribution with pre-specified factors is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the OLiP distribution’s parameters, and the truncation time, numerical results are obtained. The new distribution is illustrated using mortality rates of COVID-19 patients in Canada and vinyl chloride data in (g/L) from ground-water monitoring wells that are located in clean-up-gradient areas.

In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as $\delta =P\left[W<V\right]$, where V and W are the strength and stress random variables, respectively, and $\delta$ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of $\delta =P\left[W<V\right]$ for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of $\delta$ is derived. The Bayes estimator of $\delta$ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.

A new class of distribution called the Fréchet binomial (FB) distribution is proposed. The new suggested model is very flexible because its probability density function can be unimodal, decreasing and skewed to the right. Furthermore, the hazard rate function can be increasing, decreasing, up-side-down and reversed-J form. Important mixture representations of the probability density function (pdf) and cumulative distribution function (cdf) are computed. Numerous sub-models of the FB distribution are explored. Numerous statistical and mathematical features of the FB distribution such as the quantile function ($Q_{UN}F$); moments ($M_O$); incomplete $M_O$ ($I{M}_O$); conditional $M_O$ ($C{M}_O$); $M_O$ generating function ($M_{O}GF$); probability weighted $M_O$ ($PW{M}_O$); order statistics; and entropy are computed. When the life test is shortened at a certain time, acceptance sampling (ACS) plans for the new proposed distribution, FB distribution, are produced. The truncation time is supposed to be the median lifetime of the FB distribution multiplied by a set of parameters. The smallest sample size required ensures that the specified life test is obtained at a particular consumer’s risk. The numerical results for a particular consumer’s risk, FB distribution parameters and truncation time are generated. We discuss the method of maximum likelihood to estimate the model parameters. A simulation study was performed to assess the behavior of the estimates. Three real datasets are used to illustrate the importance and flexibility of the proposed model.