Abstract
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.
Highlights
Iqbal et al, (2017) [1] defined the Libby-Novick Kumaraswamy (LNK) distribution
After simplification we find the quantile function of the LNK distribution as under; Q(
The following tables show the numerical values with MLEs and their corresponding standard errors of the model parameters including loglikelihood, KolmogorovSmirnov test (KS), Akaike information criterion (AIC) and Consistent Akaike information criterion (CAIC) for comparing LNK distribution with the Power distribution, Beta distribution with (a =1), Beta distribution, Kumaraswamy distribution
Summary
Iqbal et al, (2017) [1] defined the Libby-Novick Kumaraswamy (LNK) distribution. The probability density function (pdf) and cumulative distribution function (cdf) are respectively defined as ( ) xa−1 1− xa b−1 f ( x) = abc 1− (1− c) xa 1+b ; 0 x 1, a, b, c 0. Libby-Novick (1982) [2] derived two new multivariate probability density functions, which are the generalized forms of beta distribution. Ristic et al, (2013) [8] derived new family of skewed distributions such as Libby and Novick’s generalized beta exponential distribution and found some useful properties of this family of distributions. Cordeiro et al, (2014) [9] defined a family of distributions, named the Libby-Novick beta family of distributions, which includes the classical beta generalized and exponentiated generators This extended family gave reasonable parametric fits to real data in several areas because the additional shape parameters controlled the skewness and kurtosis simultaneously. Ali (2019) [10] worked on new form of Libby-Novick (NLN) distribution and explored some properties of NLN distribution This model was compared with other distributions by fitting them to a real data set.
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