Fatemeh Maleki Jebely - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
Karim Zare - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
Soheil Shokri - Department of Statistics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
Parvin Karami - Department of Mathematics, Nourabad Mamasani Branch, Islamic Azad University, Nourabad Mamasani, Iran

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. (۲۰۱۳). 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 ۱, the LSPF method performs better than the others, and when the shape parameter is equal to or smaller than ۱, the ML method is better than the others.

cumulative distribution function, Maximum Likelihood Estimation, moment estimation, Probability Density Function, Weibull distribution