Inference based on partly interval censored data from a two-parameter Rayleigh distribution

In this paper, the maximum likelihood and Bayesian estimation of the parameters of location-scale Rayleigh distribution with partly interval censored data is considered. For computing the maximum likelihood estimators with partly interval censored data, three methods are used, namely, Newton-Raphson, Expectation-Maximization and Monte-Carlo Expectation-Maximization algorithms. The standard errors of the estimates are computed using the observed information matrix. Also, two types of confidence intervals are constructed using the Wald method and the nonparametric percentile bootstrap confidence intervals. For computing the Bayes estimators, three methods viz Lindley's approximation, Tierney-Kadane approximation and importance sampling methods are used. Highest posterior density (HPD) credible intervals of the two parameters are constructed using importance sampling technique. Monte-Carlo simulation experiments are conducted to investigate the performance of the proposed methods. Finally, the methods are illustrated by using two real data sets, one is related with diabetic patients data set and the other is related to HIV infection data set.