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One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution

P.O. Box 123-AA, Adelaide, SA 5000, Australia
Stats 2019, 2(1), 34-54; https://doi.org/10.3390/stats2010004
Received: 12 December 2018 / Revised: 15 January 2019 / Accepted: 18 January 2019 / Published: 21 January 2019
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Abstract

A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the level of similarity between them. The performance of the new distribution is compared to the Weibull and in some cases the Gamma distribution using real data. In addition, the Exponential distribution is modified to include an extra parameter via a simple transformation using fractional mathematics. It will be shown that the modified version also exhibits Weibull characteristics for particular values of the second parameter. View Full-Text
Keywords: relative entropy; 1D-Weibull distribution; fractional exponential distribution; Weibull distribution; gamma distribution relative entropy; 1D-Weibull distribution; fractional exponential distribution; Weibull distribution; gamma distribution
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Alexopoulos, A. One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution. Stats 2019, 2, 34-54.

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