Estimation for the generalized half-normal distribution based on progressive type-II censoring

Inference and optimal design for the k-level step-stress accelerated life test based on progressive Type-I interval censored power Rayleigh data

In this paper, a new generalization of the one parameter Rayleigh distribution called the Power Rayleigh (PRD) was employed to model the life of the tested units in the step-stress accelerated life test. Under progressive Type-I interval censored data, the cumulative exposure distribution was considered to formulate the life model, assuming the scale parameter of PRD has the inverse power function at each stress level. Point estimates of the model parameters were obtained via the maximum likelihood estimation method, while interval estimates were obtained using the asymptotic normality of the derived estimators and the bootstrap resampling method. An extensive simulation study of $ k = 4 $ levels of stress in different combinations of the life test under different progressive censoring schemes was conducted to investigate the performance of the obtained point and interval estimates. Simulation results indicated that point estimates of the model parameters are closest to their initial true values and have relatively small mean squared errors. Accordingly, the interval estimates have small lengths and their coverage probabilities are almost convergent to the 95% significance level. Based on the Fisher information matrix, the D-optimality and the A-optimality criteria are implemented to determine the optimal design of the life test by obtaining the optimum inspection times and optimum stress levels that improve the estimation procedures and give more efficient estimates of the model parameters. Finally, the developed inferential procedures were also applied to a real dataset.

Objective Bayesian Estimation for the Differential Entropy Measure Under Generalized Half-Normal Distribution

The evaluation of the information entropy content in the data analysis is an effective role in the assessment of fatigue damage. Due to the connection between the generalized half-normal distribution and fatigue extension, the objective inference for the differential entropy of the generalized half-normal distribution is considered in this paper. The Bayesian estimates and associated credible intervals are discussed based on different non-informative priors including Jeffery, reference, probability matching, and maximal data information priors for the differential entropy measure. The Metropolis-Hastings samplers data sets are used to estimate the posterior densities and then compute the Bayesian estimates. For comparison purposes, the maximum likelihood estimators and asymptotic confidence intervals of the differential entropy are derived. An intensive simulation study is conducted to evaluate the performance of the proposed statistical inference methods. Two real data sets are analyzed by the proposed methodology for illustrative purposes as well. Finally, non-informative priors for the original parameters of generalized half-normal distribution based on the direct and transformation of the entropy measure are also proposed and compared.