In this paper, we have introduced a five‐parameter bivariate model by taking a geometric minimum of the modified exponential distributions. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. A number of simulation experiments have been performed to determine the effectiveness of the proposed EM algorithm. We analyze two datasets for illustrative purposes, and it is observed that the proposed models and the expectation‐maximization algorithm perform at a satisfactory level. پرونده مقاله

The purpose of the present study is to consider the estimation of the PDF and CDF of the three-parameter inverse Weibull (IWD) distribution. To do so, we propose the following well-known methods: moment (MM) estimation, maximum likelihood (ML) estimation, and a developed method entitled the location and scale parameters free maximum likelihood (LSPF) derived from Nagatsuka et al. (2013). Having estimated the parameters, we would consider estimating the PDF and the CDF of the IWD distribution with these three methods. Then, analytical expressions are derived for the mean integrated squared error (MISE) to compare the estimators. According to the results of simulation and two real data for estimation of the PDF and CDF, when the shape parameter is greater than 1, the LSPF method performs better than the others, and when the shape parameter is equal to or smaller than 1, the ML method is better than the others. پرونده مقاله