International Journal of Nonlinear Analysis and Applications

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

Document Type : Research Paper

Authors

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

2 Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

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

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 1017-1036
  • Receive Date: 03 September 2020
  • Revise Date: 16 October 2020
  • Accept Date: 28 October 2020