Estimation of the coefficient of variation for non-normal model using progressive first-failure-censoring data

The coefficient of variation (CV) is extensively used in many areas of applied statistics including quality control and sampling. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. In this article, based on progressive first-failure-censored data, we study the behavior of the CV of a random variable that follows a Burr-XII distribution. Specifically, we compute the maximum likelihood estimations and the confidence intervals of CV based on the observed Fisher information matrix using asymptotic distribution of the maximum likelihood estimator and also by using the bootstrapping technique. In addition, we propose to apply Markov Chain Monte Carlo techniques to tackle this problem, which allows us to construct the credible intervals. A numerical example based on real data is presented to illustrate the implementation of the proposed procedure. Finally, Monte Carlo simulations are performed to observe the behavior of the proposed methods.