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

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  • Aris Alexopoulos

    (P.O. Box 123-AA, Adelaide, SA 5000, Australia)

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.

Suggested Citation

  • Aris Alexopoulos, 2019. "One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution," Stats, MDPI, vol. 2(1), pages 1-21, January.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:1:p:4-54:d:199567
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    References listed on IDEAS

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    1. Camilo Carrillo & José Cidrás & Eloy Díaz-Dorado & Andrés Felipe Obando-Montaño, 2014. "An Approach to Determine the Weibull Parameters for Wind Energy Analysis: The Case of Galicia (Spain)," Energies, MDPI, vol. 7(4), pages 1-25, April.
    2. Young Lee & Byeong Park, 2006. "Estimation of Kullback–Leibler Divergence by Local Likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 327-340, June.
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