Classical and Bayesian estimation of $$P(X>Y)$$ P ( X > Y ) using upper record values from Kumaraswamy’s distribution

Mustafa Nadar () and Fatih Kızılaslan ()

Statistical Papers, 2014, vol. 55, issue 3, 783 pages

Abstract: In this paper, maximum likelihood and Bayesian approaches have been used to obtain the estimation of $$P(X>Y)$$ P ( X > Y ) based on a set of upper record values from Kumaraswamy distribution. The existence and uniqueness of the maximum likelihood estimates of the Kumaraswamy distribution parameters are obtained. Confidence intervals, exact and approximate, as well as Bayesian credible intervals are constructed. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX) loss functions using the conjugate and non informative prior distributions. The approximation forms of Lindley (Trabajos de Estadistica 3:281–288, 1980 ) and Tierney and Kadane (J Am Stat Assoc 81:82–86, 1986 ) are used for the Bayesian cases. Monte Carlo simulations are performed to compare the different proposed methods. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Kumaraswamy distribution; Stres-strength model; Record values; Bayes estimation; Symmetric and asymmetric loss functions; 62F10; 62F15; 62N05 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00362-013-0526-x

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