Showing papers on "Kumaraswamy distribution published in 2010"
TL;DR: This work introduces and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data and provides explicit expressions for the moments and moment generating function.
Abstract: For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed.
348 citations
TL;DR: In this article, a new model for considering the balance equation of the storage volume of the reservoir using indicator functions was presented. But this model required no discretization of storage volumes or releases.
15 citations
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TL;DR: In this article, a new five-parameter continuous distribution which generalizes the Kumaraswamy and the beta distributions as well as some other well-known distributions is proposed and studied.
Abstract: A new five-parameter continuous distribution which generalizes the Kumaraswamy and the beta distributions as well as some other well-known distributions is proposed and studied. The model has as special cases new four- and three-parameter distributions on the standard unit interval. Moments, mean deviations, Renyi's entropy and the moments of order statistics are obtained for the new generalized Kumaraswamy distribution. The score function is given and estimation is performed by maximum likelihood. Hypothesis testing is also discussed. A data set is used to illustrate an application of the proposed distribution.
10 citations
TL;DR: In this article, the authors considered the case p = 1 when the marginal distribution is approximated by the power law distribution closely connected with the Kumaraswamy distribution, and they proved that for p ∈ (0, 1), the innovation process has a uniform discrete distribution.
Abstract: We consider the AR(1) time series model Xt − βXt−1 = ξt, β−p ∈ N \ {1}, when
Xt has Beta distribution B(p, q), p ∈ (0, 1], q > 1. Special attention is
given to the case p = 1 when the marginal distribution is approximated by
the power law distribution closely connected with the Kumaraswamy
distribution Kum(p, q), p ∈ (0, 1], q > 1. Using the Laplace transform
technique, we prove that for p = 1 the distribution of the innovation
process is uniform discrete. For p ∈ (0, 1), the innovation process has a
continuous distribution. We also consider estimation issues of the model.
7 citations
TL;DR: In this paper, the authors considered the mixed A R (1) time series model with the two-parameter Kumaraswamy distribution and showed that the distribution of the innovation process is uniform discrete.
7 citations