Comparisons of Methods of Estimation for the NH Distribution

The extended exponential distribution due to Nadarajah and Haghighi (Stat J Theor Appl Stat 45(6):543–558, 2011) is an alternative and always provides better fits than the gamma, Weibull and the generalized exponential distributions whenever the data contains zero values. This article addresses different methods of estimation of the unknown parameters from both frequentist and Bayesian view points of Nadarajah and Haghighi (in short NH ) distribution. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moment estimators, percentile estimators, least square and weighted least square estimators and compare them using extensive numerical simulations. Next we consider Bayes estimation under different types of loss functions (symmetric and asymmetric loss functions) using gamma priors for both shape and scale parameters. Besides, the asymptotic confidence intervals, two parametric bootstrap confidence intervals using frequentist approaches are provided to compare with Bayes credible intervals. Furthermore, the Bayes estimators and their respective posterior risks are computed and compared using Markov chain Monte Carlo algorithm. Finally, two real data sets have been analyzed for illustrative purposes.