Libby-Novick Kumaraswamy Distribution with Its Properties and Applications

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Abdul Saboor
Zafar Iqbal
Muhammad Hanif
Munir Ahmad


The Kumaraswamy distribution is one of the most popular probability distributions with applications to real life data. In this paper, an extension of this distribution called the Libby-Novick Kumaraswamy (LNK) distribution is presented which is believed to provide greater flexibility to model scenarios involving skew-normal data than original one. Analytical expressions for various mathematical properties including its cdf, quantile function, moments, factorial moments, conditional momennts, moment generating function, characteristic function, vitality function, information generating function, reliability measures, mean deviations, mean residual function, Bonferroni and Lorenz Curves are derived.The parameters' estimation of LNK distribution is undertaken using the method of maximum likelihood estimation. A simulation study for different values of sample sizes, to assess the performance of the parameters of LNK distribution is provided.  For illustration and performance evaluation of LNK distribution three real-life data sets from the field of engineering and science adapted from earlier studies are used. On comparing the results to previously used methods, LNK distribution shows that it can give consistently better fit than other existing important lifetime models. It is found that the LNK distribution is more suitable and useful to study lifetime data.

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