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Inferences on the Weibull Exponentiated Exponential Distribution and Applications
International Journal of Statistical Distributions and Applications
Volume 6, Issue 1, March 2020, Pages: 10-22
Received: Nov. 6, 2019; Accepted: Dec. 20, 2019; Published: Jul. 15, 2020
Authors
Umar Usman, Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
Suleiman Shamsuddeen, Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
Bello Magaji Arkilla, Department of Community Health, Usmanu Danfodiyo University, Sokoto, Nigeria
Yakubu Aliyu, Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
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Abstract
In this article, an alternative method of defining the probability density function of GeneralizedWeibull-exponential distributions is proposed. Based on the method, the distribution can also be calledWeibull exponentiated exponential distribution. This distribution includes the exponential, Weibull and exponentiated exponential distributions as special cases. Comprehensive mathematical treatment of the distribution is provided. The quantile function, mode, characteristic function, moment generating function among other mathematical properties of the distribution were derived. The parameters of the distribution were estimated by applying the Maximum Likelihood Procedure.The elements of the Fisher Information Matrix is also provided. Finally, a data set is fitted to the model and its sub-models. It is observed that the new distribution is more flexible and can be used quiet effectively in analysing real life data in place of exponential, Weibull and exponentiated exponential distributions.
Keywords
T-X Family, Exponentiated Exponential Distribution, Order Statistics, Shannon Entropy and Likelihood Ratio Test
Umar Usman, Suleiman Shamsuddeen, Bello Magaji Arkilla, Yakubu Aliyu, Inferences on the Weibull Exponentiated Exponential Distribution and Applications, International Journal of Statistical Distributions and Applications. Vol. 6, No. 1, 2020, pp. 10-22. doi: 10.11648/j.ijsd.20200601.12
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