Validation of Xgamma Exponential Model via Nikulin-Rao-Robson Goodness-of- Fit-Test under Complete and Censored Sample with Different Methods of Estimation

Abstract

In this article, a new extension of the one parameter Xgamma distribution has been proposed. Also the associated different statistical properties are derived. The unknown parameter of the proposed distribution is estimated by using different classical estimation methods and by using Bayesian estimation method. Under classical methods of estimation, we brieflfly describe the method of moment estimators, maximum likelihood estimators, maximum product of spacing estimators, least squares and weighted least squares estimators and Cramer-von-Mises estimators. The Bayesian estimation using gamma prior under squared error loss function has been discussed and computed via Lindley’s approximation and Markov Chain Monte Carlo techniques. Furthermore, the 100(1 − α)% asymptotic confifidence interval and credible interval along with the coverage probability are also discussed. The obtained classical and the Bayesian estimators are compared through Monte Carlo simulations. Next, we construct a modifified Chi-squared goodness of fifit test based on the Nikulin-Rao-Robson (NRR) statistic in presence of censored and complete data. The applicability of our proposed model has been illustrated for both complete data and right censored data by using two real data sets for each.