Classical and Bayesian estimation of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$P(X>Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>></mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> using upper record values from ...

In this paper, maximum likelihood and Bayesian approaches have been used to obtain the estimation of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$P(X>Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>></mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> 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, <CitationRef CitationID="CR25">1980</CitationRef>) and Tierney and Kadane (J Am Stat Assoc 81:82–86, <CitationRef CitationID="CR38">1986</CitationRef>) are used for the Bayesian cases. Monte Carlo simulations are performed to compare the different proposed methods. Copyright Springer-Verlag Berlin Heidelberg 2014