The logarithmic Kumaraswamy family of distributions: properties and applications
Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1335-1352
Published online October 31, 2019
Zubair Ahmad
Quaid-i-Azam University
Abstract : In this article, a new family of lifetime distributions by adding two additional parameters is introduced. The new family is called, the logarithmic Kumaraswamy family of distributions. For the proposed family, explicit expressions for some mathematical properties are derived. Maximum likelihood estimates of the model parameters are also obtained. This method is applied to develop a new lifetime model, called the logarithmic Kumaraswamy Weibull distribution. The proposed model is very flexible and capable of modeling data with increasing, decreasing, unimodal or modified unimodal shaped hazard rates. To access the behavior of the model parameters, a simulation study has been carried out. Finally, the potentiality of the new method is proved via analyzing two real data sets.
Keywords : family of distributions, Weibull distribution, moments, order statistic, residual life function, maximum likelihood estimation
MSC numbers : Primary 60E05, 62F10
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