BAYESIAN ESTIMATION OF TOPP-LEONE LINDLEY (TLL) DISTRIBUTION PARAMETERS UNDER DIFFERENT LOSS FUNCTIONS USING LINDLEY APPROXIMATION.

In this study, we present the Bayesian estimates of the unknown parameters of the Topp-Leone Lindley distribution using the maximum likelihood and Bayesian methods. In this study, the Bayes theorem was adopted for obtaining the posterior distribution of the shape parameter and scale parameter of the Topp-Leone Lindley distribution assuming the Jeffreys' (non-informative) prior for the shape parameter and the Gamma (conjugate) prior for the scale parameter under three different loss functions namely: Square Error Loss Function, Linear Exponential Loss Function and Generalized Entropy Loss Function. The posterior distribution derived for both parameters are not solvable analytically, it requires a numerical approximation techniques to obtain the solution. The Lindley approximation techniques was adopted to obtain the parameters of interest. The loss function were used to derive the estimates of both parameters with an assumption that the both parameters are unknown and independent. To ascertain the accuracy of these estimators, the proposed Bayesian estimators under different loss functions are compared with the corresponding maximum likelihood estimator using a Monte Carlo simulation on the performance of these estimators according to the mean square error and BIAS based on simulated samples simulated from the Topp-Leone Lindley distribution.. It was also observed for any fixed value of the parameters, as sample size increases, the mean square errors of the Bayesian Estimates and maximum likelihood estimates decrease. Also, the maximum likelihood estimates and Bayesian estimates converge to the same value as the sample gets larger except for Generalized Entropy Loss Function. [ABSTRACT FROM AUTHOR]