Comparison of Estimators of the PDF and the CDF of the Three-Parameter Inverse Weibull Distribution

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.