Open Access
August 2015 Estimates of the PDF and the CDF of the exponentiated Weibull distribution
M. Alizadeh, S. F. Bagheri, E. Baloui Jamkhaneh, S. Nadarajah
Braz. J. Probab. Stat. 29(3): 695-716 (August 2015). DOI: 10.1214/14-BJPS240


Exponentiated Weibull distribution, introduced as an extension of the Weibull distribution, is characterized by bathtub shaped, unimodal failure rates besides a broader class of monotone failure rates. In this paper, we derive maximum likelihood estimators (MLEs), uniformly minimum variance unbiased estimators and three other estimators of the probability density function and the cumulative distribution function of the exponentiated Weibull distribution and compare their performances through numerical simulations. Simulation studies show that the MLE is more efficient than the others. Analysis of a real data set is presented for illustrative purposes.


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M. Alizadeh. S. F. Bagheri. E. Baloui Jamkhaneh. S. Nadarajah. "Estimates of the PDF and the CDF of the exponentiated Weibull distribution." Braz. J. Probab. Stat. 29 (3) 695 - 716, August 2015.


Received: 1 August 2013; Accepted: 1 February 2014; Published: August 2015
First available in Project Euclid: 11 June 2015

zbMATH: 1326.62032
MathSciNet: MR3355754
Digital Object Identifier: 10.1214/14-BJPS240

Keywords: exponentiated Weibull distribution , least squares estimator , maximum likelihood estimator , model selection criteria , percentile estimator , uniformly minimum variance unbiased estimator , weighted least squares estimator

Rights: Copyright © 2015 Brazilian Statistical Association

Vol.29 • No. 3 • August 2015
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