The extended reduced Kies distribution (ExRKD), which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well‐known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID‐19 and milk data sets, which demonstrates that the ExRKD delivers a better match to the data sets when compared to competing models.

The aim of this paper is to specify a new flexible statistical model to analyze COVID-19 mortality rates in Italy and Canada. A new versatile lifetime distribution with four parameters is proposed by using the exponentiated generalized class of distributions and the gull alpha power Rayleigh distribution to form the exponentiated generalized gull alpha power Rayleigh (EGGAPR) distribution. This new distribution is characterized by a tractable cumulative distribution function. To estimate the unknown parameters of the proposed distribution the maximum likelihood estimation method is used. In evaluating the effectiveness of the MLE method graphical displays of the Monte Carlo simulation are presented. The EGGAPR distribution is compared to its sub-models which include the exponentiated gull alpha Rayleigh distribution, the gull alpha Rayleigh distribution, exponentiated generalized Rayleigh distribution, exponentiated Rayleigh distribution and the Rayleigh distribution. Different measures of goodness-of-fit are used to investigate whether the EGGAPR distribution is more flexible and fit than its sub-models in modeling COVID-19 mortality rates.

In this paper, a bivariate power Lomax distribution based on Farlie-Gumbel-Morgenstern (FGM) copulas and univariate power Lomax distribution is proposed, which is referred to as BFGMPLx. It is a significant lifetime distribution for modeling bivariate lifetime data. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, product moments, positive quadrant dependence property, and Pearson’s correlation, have been studied. The reliability measures, such as the survival function, hazard rate function, mean residual life function, and vitality function, have also been discussed. The parameters of the model can be estimated through maximum likelihood and Bayesian estimation. Additionally, asymptotic confidence intervals and credible intervals of Bayesian’s highest posterior density are computed for the parameter model. Monte Carlo simulation analysis is used to estimate both the maximum likelihood and Bayesian estimators.

This paper proposes a new generalization of the Gull Alpha Power Family of distribution, namely the exponentiated generalized gull alpha power family of distribution abbreviated as (EGGAPF) with two additional parameters. This proposed family of distributions has some well known sub-models. Some of the basic properties of the distribution like the hazard function, survival function, order statistics, quantile function, moment generating function are investigated. In order to estimate the parameters of the model the method of maximum likelihood estimation is used. To assess the performance of the MLE estimates a simulation study was performed. It is observed that with increase in sample size, the average bias, and the RMSE decrease. A distribution from this family is fitted to two real data sets and compared to its sub-models. It can be concluded that the proposed distribution outperforms its sub-models.

We hope to assess the different processing methodologies or the effectiveness of the devices or systems applied in this nonparametric statistical test by observing the failure behavior of the recorded survival data. The proposed second-order approach of new better than used (NBU 2) will be employed, which requires that the test data behaves either like NBU 2 property or exponentially. If the survival data is NBU 2, the proposed treatment method is likely to be beneficial. If the data are exponential, on the other hand, the recommended treatment method has no positive or negative influence on patients, as shown in the application section. To establish the validity of the test, we calculated the power of the proposed test and efficiency on both complete and censored data, compared the results to those of existing tests, and then applied the test to a range of real-world data.

The objective of this study is to construct a new distribution known as the weighted Burr–Hatke distribution (WBHD). The PDF and CDF of the WBHD are derived in a closed form. Moments, incomplete moments, and the quantile function of the proposed distribution are derived mathematically. Eleven estimate techniques for estimating the distribution parameters are discussed, and numerical simulations are utilised to evaluate the various approaches using partial and overall rankings. According to the findings of this study, it is recommended that the maximum product of spacing (MPSE) estimator of the WBHD is the best estimator according to overall rank table. The actuarial measurements were derived to the suggested distribution. By contrasting the WBHD with other competitive distributions using two different actual data sets collected from the COVID-19 mortality rates, we show the importance and flexibility of the WBHD.