Title

Weighted Generalizations of the Generalized Rayleigh Distribution With Applications

Document Type

Article

Publication Date

8-2015

Publication Title

Journal of Probability and Statistical Sciences

ISSN

1726-3328

Abstract

In this paper, weighted generalizations of the generalized Rayleigh distribution is proposed and studied in detail. We present the statistical properties of the weighted generalized Rayleigh distribution with the weight function
w(x) = xk exp{txβ}Fi (x)-Fj (x)
when i = j = 0. In particular, we derive the probability density function (pdf), cumulative distribution function (cdf), hazard function, reverse hazard function, moments, coeffcients of variation, skewness and kurtosis. Shannon entropy, Renyi entropy, β-entropy, generalized entropy and Fisher information are derived. Maximum likelihood estimates of the model parameters are also presented. Test procedures for weightedness including length-biasedness concerning the Rayleigh, generalized Rayleigh and weighted generalized Rayleigh models are developed. Real data examples are given to illustrate the usefulness of the proposed distribution.

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