On Some Estimation Methods for the Inverse Pareto Distribution

There are many real-life situations, where data require probability distribution function which have decreasing or upside down bathtub (UBT) shaped failure rate function. The inverse Pareto distribution consists both decreasing and UBT shaped failure rate functions. Here, we address the different estimation methods of the parameter and reliability characteristics of the inverse Pareto distribution from both classical and Bayesian approaches. We consider several classical estimation procedures to estimate the unknown parameter of inverse Pareto distribution, such as maximum likelihood, method of percentile, maximum product spacing, the least squares, weighted least squares, Anderson–Darling, right-tailed Anderson–Darling and Cramér–Von-Mises. Also, we consider Bayesian estimation using squared error loss function based on conjugate and Jefferys’ priors. An extensive Monte Carlo simulation experiment is carried out to compare the performance of different estimation methods. For illustrative purposes, we have considered two real data sets.