Parameters estimation approaches of the Moore and Bilikam family with reliability analysis under progressively type-II censoring

Abstract

The precise investigation of the Moore and Bilikam (MB) family of distributions is essential since they cover several distributions as special cases. We evaluate different estimation procedures for parameters of MB family comprehensively. Moreover, the confidence interval and highest posterior density interval estimators of parameters are provided. The different estimation methods of the parameters of two certain cases of the MB family are compared via the simulation data. Based on the simulation approach, we realized the estimates are convergent to the real values of the parameters and the root mean squared error (RMSE) values derived by the expectation-maximization (EM) algorithm are less than Newton–Raphson (NR), stochastic EM (SEM) and Bayes estimators. Also, the higher values of the sample size lead to better estimates in the sense close to true parameter values and having smaller RMSE values. The reliability analysis of MB family is another topic in this paper, with simulation discussion. The Monte Carlo simulations are provided to assess the performances of estimation methods. We concluded the Bayesian shrinkage estimators are better than other methods of the reliability function, which have the smallest values of the RMSE. The analysis of real dataset has been presented for illustrative purposes, which confirmed simulation results.