UDC 519.2 © Ramin Gholizadeh, Aliakbar M. Shirazi BAYES ESTIMATOR OF KUMARASWAMY DISTRIBUTION IN THE PRESENCE OUTLIERS USING LINDLEY'S APPROXIMATION In this paper, the maximum likelihood and the Bayes estimators under symmetric and asymmetric loss functions are derived for sample from the Kumaraswamy distribution in the presence of outliers, using Newton-Raphson method and Lindley's approximation (L-approximation). <...> These estimators are compared empirically using Monte Carlo simulation, when all the parameters are unknown. <...> Keywords: Bayesian inference, Maximum Likelihood Estimator, LINEX loss function, Kumaraswamy distribution, outliers, Lindley's approximation, Newton-Raphson method, Monte-Carlo simulation. 1. <...> The probabi l ity density function of a Kumaraswamy distributed random variable is given by (1) where and are shape parameters, respectively. <...> Here we assume that parameter is known. <...> It may also be noted here that the squared-error loss function can be obtained as a particular member of the LINEX loss function for a specific choice of the loss function parameter. <...> However, Bayesian estimation under the LINEX loss function is not frequently discussed, perhaps, because the estimators under asymmetric loss function involve integral expressions, which are not analytically solvable. <...> In section 2, we have obtained the joint distribution section 3, we derive the MLE of and . <...> The Bayes estimators of and have been presented in section 4. <...> The different proposed methods have been compared using Monte Carlo simulations and the results have been repor ted in section 5 and final ly we draw conclusions in section 6. of (X1, X2, …, Xn ) in the presence of k outliers. <...> This joint distribution must satisfy the following ) Ramin Gholizadeh, Aliakbar M. Shirazi (8) (14) Since we will need some derivatives of , with respect to and , in the rest of the paper, we will define some of them followings : (9) (10) (15) (11) (16) (12) , (13) (17) 72 Проблемы машиностроения и автоматизации, № 4 – 2011 BAYES ESTIMATOR OF KUMARASWAMY DISTRIBUTION IN THE PRESENCE OUTLIERS USING LINDLEY'S APPROXIMATION 3. <...> Suppose (x1 from the density function defined in (7). <...> Thus, one of the is MLE of , By Newton-Raphson method, solution of the above equation is <...>