Tolerance intervals and confidence intervals for the scale parameter of Pareto-Rayleigh distribution

In this paper we consider interval estimation in Pareto-Rayleigh distribution as an example of a Transformed-Transformer family of distribution defined by Alzaatreh et. al (2012). We construct confidence intervals (CIs) and tolerance intervals (TIs) using generalized variable (GV) approach by using maximum likelihood estimator (MLE) and modified maximum likelihood estimator (MMLE) as the likelihood equations are intractable (Tiku and Suresh (1992)). Performances of both intervals are studied using simulation and compared them with existing ones to check superiority of the proposed method. The confidence intervals and tolerance intervals are illustrated through real life data.