Abstract
A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) distribution is proposed and studied. This family includes several well known sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the sub-models are presented. Maximum likelihood estimates of the model parameters are obtained. Simulation studies are conducted. Examples and applications as well as comparisons of the EKD and its sub-distributions with other distributions are given.Mathematics Subject Classification (2000)62E10; 62F30
Highlights
Camilo Dagum proposed the distribution which is referred to as Dagum distribution in 1977
3 The exponentiated Kumaraswamy-Dagum distribution we present the proposed distribution and its sub-models
The mean of the exponentiated Kumaraswamy-Dagum (EKD) distribution is obtained from equation (10) with s = 1 and the quantile function is given in equation (5)
Summary
Camilo Dagum proposed the distribution which is referred to as Dagum distribution in 1977. The pdf and cumulative distribution function (cdf ) of Dagum distribution are given by: gD(x; λ, β, δ) = βλδx−δ−1 1 + λx−δ −β−1. We present generalizations of the Dagum distribution via Kumaraswamy distribution and its exponentiated version. 2 Methods, results and discussions Methods, results and discussions for the class of EKD distributions are presented in sections 3 to 8 These sections include the sub-models, series expansion of the pdf, closed form expressions for the hazard and reverse hazard functions, moments, moment generating function, Bonferroni and Lorenz curves, reliability, mean and median deviations, distribution of order statistics and entropy, as well as estimation of model parameters and applications. For the EKD(α, λ, δ, φ, θ) distribution, α is shape and skewness parameter, δ is shape parameter, λ is a scale parameter, φ is a tail variation parameter, and the parameter θ characterizes the skewness, kurtosis, and tail of the distribution
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