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Dr. Ahmed Z. Afify :: Publications:

A New Extension of Weibull Distribution: Properties and Different Methods of Estimation
Authors: Mazen Nassar; Ahmed Z. Afify; Sanku Dey; Devendra Kumar
Year: 2017
Keywords: Weibull distributionك Momentsك Quantile functionكStochastic orderingك Entropy;Stress-strength reliability;Parameter estimation
Journal: Journal of Computational and Applied Mathematics
Volume: Not Available
Issue: Not Available
Pages: forthcoming
Publisher: Elsevier Editorial System
Local/International: International
Paper Link: Not Available
Full paper Not Available
Supplementary materials Not Available

The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization of the Weibull distribution, called Alpha logarithmic transformed Weibull distribution that provides better ts than some of its known generalizations. The proposed distribution contains Weibull, exponential, logarithmic transformed exponential and logarithmic transformed Weibull distributions as special cases. Our main focus is the estimation from frequentist point of view of the unknown parameters along with some mathematical properties of the new model. The proposed distribution accommodates monotonically increasing, decreasing, bathtub and unimodal and then bathtub shape hazard rates, so it turns out to be quite exible for analyzing non-negative real life data. We brie y describe di erent frequentist approaches, namely, maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets.

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