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

Subject Areas : International Journal of Mathematical Modelling & Computations

Fatemeh Maleki Jebely ¹ , Karim Zare ² , Soheil Shokri ³ , Parvin Karami ⁴

1 - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
2 - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
3 - Department of Statistics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
4 - Department of Mathematics, Nourabad Mamasani Branch, Islamic Azad University, Nourabad Mamasani, Iran

Received: 2021-07-06 Accepted : 2022-03-13 Published : 2022-09-15

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

Abstract :

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.