Some estimation procedures of the PDF and CDF of the generalized inverted Weibull distribution with comparison

Document Type : Research Paper

Authors

1 Islamic Azad university

2 Department of Statistics, Qaemshahr Branch, IslamicAzad University, Qaemshahr, Iran

10.22075/ijnaa.2020.21419.2257

Abstract

Different estimation procedures for the probability density and cumulative distribution functions
of the generalized inverted Weibull distribution are discussed. For this purpose, the parametric and non-parametric estimation approaches as maximum likelihood, uniformly minimum variance unbiased, percentile, least squares and weighted least squares estimators are considered and compared. The expectations and mean square error of the maximum likelihood and uniformly minimum variance unbiased estimation are provided in the closed-form whereas, for non-parametric estimation methods (percentile, least squares and weighted least squares), the expectations and mean square error are computed via the simulation data. The Monte Carlo simulations are provided to assess the performances of the proposed estimation methods. Finally, the analysis of the real data set has been presented for illustrative purposes.

Keywords