Abstract
We propose and study a new five-parameter continuous distribution in the unit interval through a specific probability integral transform. The new distribution, under some parameter constraints, is an identified parametric model that includes as special cases six important models such as the Kumaraswamy and beta distributions. We obtain ordinary and incomplete moments, quantile and generating functions, mean deviations, R\'enyi entropy and moments of order statistics. The estimation of the model parameters is performed by maximum likelihood, and hypothesis tests are discussed. Additionally, through a simulation study we investigate the behavior of the maximum likelihood estimator, also we investigate the impact of ignoring identifiability problems. The usefulness of the proposed distribution is illustrated by means of a real data set.
Highlights
We define and study a new five-parameter distribution called the extended Kumaraswamy (EKw) distribution that includes, as special models, some well-known distributions such as the Kumaraswamy (Kw, for short) and beta (B) distributions
We propose a new five-parameter continuous distribution on the standard unit interval that generalizes the beta, Kumaraswamy (Kumaraswamy, 1980), and McDonald (McDonald, 1984) distributions and includes, as special models, other distributions discussed in the literature
We demonstrate that the EKw density function can be expressed as linear combinations of Kumaraswamy and power density functions
Summary
We define and study a new five-parameter distribution called the extended Kumaraswamy (EKw) distribution that includes, as special models, some well-known distributions such as the Kumaraswamy (Kw, for short) and beta (B) distributions. Nadarajah and Kotz (2004) defined the beta Gumbel distribution by taking G1(x; ω) to be the Gumbel cdf and provided explicit expressions for the moments and the asymptotic distribution of the extreme order statistics. Nadarajah and Gupta (2004) introduced the beta Frechet distribution by taking G1(x; ω) to be the Frechet distribution, derived the analytical shapes of its density and hazard rate functions, and obtained the asymptotic distribution of its extreme order statistics. We propose an extension of the Kw distribution by taking G1(x; ω) as the cdf (3) and g2(x; τ ) as the generalized beta density of the first kind (GB1) Gupta and Nadarajah (2004a); McDonald (1984) defined by g2(x; τ ) =.
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