Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 1 2021 05 01 Some estimation procedures of the PDF and CDF of the generalized inverted Weibull distribution with comparison 1017 1036 4957 10.22075/ijnaa.2020.21419.2257 EN Mortaza Ghasemi Cherati Department of Statistics, Qaemshahr Branch, IslamicAzad University, Qaemshahr, Iran Ezzatallah Baloui Jamkhaneh Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran Einolah Deiri Department of Statistics, Qaemshahr Branch, IslamicAzad University, Qaemshahr, Iran Journal Article 2020 09 03 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. Generalized inverted Weibull distribution Maximum likelihood estimator Uniformly minimum variance unbiased estimator Percentile estimator Least squares estimator Weighted least squares estimator https://ijnaa.semnan.ac.ir/article_4957_10dfb4530f479587790b1f76f96f0f63.pdf