In this paper, the estimation of the parameters of extended Marshall-Olkin inverse-Pareto (EMOIP) distribution is studied under complete and censored samples. Five classical methods of estimation are adopted to estimate the parameters of the EMOIP distribution from complete samples. These classical estimators include the percentiles estimators, maximum likelihood estimators, least squares estimators, maximum product spacing estimators, and weighted least-squares estimators. The likelihood estimators of the parameters under type-I and type-II censoring schemes are discussed. Simulation results were conducted, for various parameter combinations and different sample sizes, to compare the performance of the EMOIP estimation methods under complete and censored samples. Further, the mean square errors, asymptotic confidence interval, average interval length, and coverage percentage are calculated under the two censored schemes. The simulation results illustrate that the coverage probabilities of the confidence intervals increase to the nominal levels when the sample size increases. A real data set from the insurance field is analyzed for illustrative purposes. The data represent monthly metrics on unemployment insurance from July 2008 to April 2013 and contain 21 variables and particularly we study the variable number 11 in the data. The EMOIP model provides a better fit as compared with the inverse-Pareto distribution under complete and censored schemes. We hope that the EMOIP distribution will attract wider applications in the insurance field which contains several heavy-tailed real data. |
