Showing papers on "Kumaraswamy distribution published in 2011"

A new family of generalized distributions

Abstract: Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with a...

The Kumaraswamy Distribution: Median-Dispersion Re-Parameterizations for Regression Modeling and Simulation-Based Estimation

Abstract: The Kumaraswamy distribution is very similar to the Beta distribution, but has the important advantage of an invertible closed-form cumulative distribution function. The parameterization of the distribution in terms of shape parameters and the lack of simple expressions for its mean and variance hinder, however, its utilization with modeling purposes. The paper presents two median-dispersion reparameterizations of the Kumaraswamy distribution aimed at facilitating its use in regression models in which both the location and the dispersion parameters are functions of their own distinct sets of covariates, and in latent-variable and other models estimated through simulation-based methods. In both re-parameterizations the dispersion parameter establishes a quantile-spread order among Kumaraswamy distributions with the same median and support. The paper also describes the behavior of the re-parameterized distributions, determines some of their limiting distributions, and discusses the potential comparative advantages of using them in the context of regression modeling and simulation based estimation

Improved point estimation for the Kumaraswamy distribution

Abstract: We develop nearly unbiased estimators for the Kumaraswamy distribution proposed by Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J Hydrol 46 (1980), pp 79–88], which has considerable attention in hydrology and related areas We derive modified maximum-likelihood estimators that are bias-free to second order As an alternative to the analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap We conduct Monte Carlo simulations in order to investigate the performance of the corrected estimators The numerical results show that the bias correction scheme yields nearly unbiased estimates

Another Generalization of the Skew Normal Distribution

Abstract: In this paper, we first introduce a new family of distributions, called Minimax Normal distributions, by using Kumaraswamy distribution. Then we use this family to find a generalization of the Balakrishnan skew-normal distribution by the name of skew minimax Normal distribution and we study some of its properties.

Kumaraswamy and beta distribution are related by the logistic map

Abstract: The Kumaraswamy distribution has been proposed as an alternative to the beta distribution with more benign algebraic properties. They have the same two parameters, the same support and qualitatively similar shape for any parameter values. There is a generic relationship between the distributions established by a simple transformation between arbitrary Kumaraswamy-distributed random variables and certain beta-distributed random variables. Here, a different relationship is established by means of the logistic map, the paradigmatic example of a discrete non-linear dynamical system.