Bayesian estimation of two-parameters Rayleigh-logarithmic using Lindley approximation

Rayleigh-Logarithmic distribution is used in survival analysis. The main objective of this study is to determine the best estimator for the parameters of this distribution. Estimation methods proposed are Lindley's method under Bayesian framework with two different loss functions; squared error loss function (SELF) and linear exponential loss (LINEX) function and maximum likelihood estimation (MLE). Through a simulation study, the performance of the proposed estimators is compared with respect to their corresponding root mean square error (RMSE). Estimator under SELF is found to be performing better than the estimator under LINEX loss function and the MLE estimators. In conclusion, the estimated parameter under squared error loss function (SELF) is comparatively the best compared to linear exponential (LINEX) loss function and maximum likelihood estimation (MLE).

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