Bayesian Estimation of Kumaraswamy Distribution under Different Loss Functions.
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Professional Statisticians Society of Nigeria(PSSN).
Abstract
In this study, the procedures of Bayesian estimation of the shape parameter of the Kumaraswamy distribution
under different prior distributions are examined. The shape parameter of the Kumaraswamy distribution is
assumed to follow noninformative prior distributions (such as the extension of Jeffrey’s prior distribution,
Hartigan Prior distribution, and Uniform Prior distribution) and the informative prior distribution (such as
the Gamma distribution and Inverted levy distribution) were adopted in this work. We compared the obtained
estimates using their mean square errors under different loss functions (such as precautionary loss function,
Squared error loss function, and Albayyati’s loss function). The results showed that the behaviour of the
Bayesian estimations of the shape parameter of the Kumaraswamy distribution under the Squared Error loss
function using Inverted levy prior distribution is the best among all the prior distributions considered.
Description
Keywords
Gamma distribution, Jeffrey’s prior, Kumaraswamy distribution, Hartigan Prior, Inverted levy distribution, Uniform Prior, Mean Square Error, Loss Function.