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

Aris Alexopoulos
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Aris Alexopoulos: P.O. Box 123-AA, Adelaide, SA 5000, Australia

Stats, 2019, vol. 2, issue 1, 1-21

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.

Keywords: relative entropy; 1D-Weibull distribution; fractional exponential distribution; Weibull distribution; gamma distribution (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2019
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