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

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Abstract

In this paper, maximum likelihood and Bayesian approaches have been used to obtain the estimation of \(P(X<Y)\) 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.

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  1. Department of Mathematics, Gebze Institute of Technology, Gebze, Turkey

    Mustafa Nadar & Fatih Kızılaslan

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  1. Mustafa Nadar
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  2. Fatih Kızılaslan
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Correspondence to Mustafa Nadar.

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Nadar, M., Kızılaslan, F. Classical and Bayesian estimation of \(P(X<Y)\) using upper record values from Kumaraswamy’s distribution. Stat Papers 55, 751–783 (2014). https://doi.org/10.1007/s00362-013-0526-x

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  • DOI: https://doi.org/10.1007/s00362-013-0526-x

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