Estimation of the reliability function for two-parameter exponentiated Rayleigh or Burr type X distribution

Problem Statement: The two-parameter exponentiated Rayleigh distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The uniformly minimum variance unbiased and maximum likelihood estimation methods are the ways to estimate the parameters of the distribution. In this study, we explore and compare the performance of the uniformly minimum variance unbiased and maximum likelihood estimators of the reliability functions R(t) = P (X > t) and P = P (X > Y ) for the two-parameter exponentiated Rayleigh distribution. Approach: A new technique of obtaining the estimators of these parametric functions is introduced in which major role is played by the estimators of powers of the parameter(s) and the functional forms of the parametric functions to be estimated are not needed. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the bias, mean square error (MSE), 95% confidence length and corresponding coverage percentage. Conclusion: Based on the results of simulation study, the uniformly minimum variance unbiased estimators of R(t) and ‘P ’ for the twoparameter exponentiated Rayleigh distribution are found to be superior than maximum likelihood estimators of R(t) and ‘P ’.