Kumaraswamy distribution; stress-strength; reversed hazard rate function; censored sampling; maximum likelihood method; asymptotic information matrix.

In this paper, exponentiated-G family of distributions is constructed as a new family of discrete distribution, using the general approach of discretization of a continuous distribution. Some statistical properties including quantiles, mean residual life, mean time to failure, mean time between failure, availability, Re ́nyi entropy, moments and order statistics are obtained. Discrete exponentiated inverted Topp–Leone distribution as a member of this family is studied in detail. Maximum likelihood approach is applied under Type-II censored sample for estimating the unknown parameters of the exponentiated inverted Topp–Leone distribution. Also, maximum likelihood estimators of the survival, hazard rate and alternative hazard rate functions are derived. The confidence intervals for the parameters, survival, hazard rate and alternative hazard rate functions are obtained. A simulation study is performed to investigate the accuracy of the theoretical results. Finally, two real data sets are analyzed to illustrate the flexibility and applicability of the proposed model for real-life applications.

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

In this paper, a discrete inverted Kumaraswamy distribution; which is a discrete version of the continuous inverted Kumaraswamy variable, is derived using the general approach of discretization of a continuous distribution. Some important distributional and reliability properties of the discrete inverted Kumaraswamy distribution are obtained. Maximum likelihood and Bayesian approaches are applied to estimate the model parameters. A simulation study is carried out to illustrate the theoretical results. Finally, a real data set is applied.

This paper introduces a new family of continuous distributions, the mixture of two components from the new Topp-Leone-G family. Statistical properties of the proposed family are explored, with a focus on the mixture of two new Topp-Leone exponential distributions as a sub-model. The study uses maximum likelihood and Bayesian methods under Type-II censoring to estimate the unknown parameters, reliability, and hazard rate functions. A simulation study evaluates the performance of the estimators. Finally, two real data sets are utilized to validate the simulated results and demonstrate the practical applicability of the proposed distribution in real life.

In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Chen-Burr XII distribution are discussed and some new models as sub-models from the Chen-Burr XII distribution are introduced. Moreover, maximum likelihood estimation of the parameters, reliability, hazard rate and reversed hazard rate functions of the Chen-Burr XII distribution are considered. Also, the asymptotic confidence intervals of the distribution parameters, reliability, hazard rate and reversed hazard rate functions are presented. Finally, three real life data sets are applied to prove how the Chen-Burr XII distribution can be applied in real life and to confirm its superiority over some existing distributions.