In medical studies or in reliability analysis, it is quite common that the failure of any individual or any item may be attributable to more than one cause. So in this paper, we consider the competing risks model with very general censoring scheme, namely progressive first-failure censored scheme under the Gompertz life time distribution. The results in each of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are a special cases. We provide different methods for the analysis of the model under the assumption of independent causes of failure and Gompertz distribution lifetimes. The maximum likelihood estimators (MLE’s) of the different parameters as well as approximate confidence intervals are presented. Bayesian estimation using MCMC method under the joint prior density as a product of a conditional gamma density and inverted gamma density for unknown Gompertz parameters are presented. The analysis of a real data set to assess the performance of all these estimators, confidence intervals are developed using asymptotic distributions and Bayesian credible intervals for the parameters. The different methods are compared through a simulation study.

The coefficient of variation (CV) of a population is defined as the ratio of the population standard deviation to the population mean. In applied statistics, the CV is widely used. However, inference concerning the coefficient of variation of non-normal distributions are rarely reported. So in this paper, Bayesian and non-Bayesian approach is adopted to estimate coefficient of variation (CV) of Topp-Leone distribution (TLD) under an adaptive Type-II Progressive Censoring Scheme. This approach will give us a point estimate as well as the empirical sampling distribution of CV. The results in the cases of progressive Type II censoring, Type II censoring and complete sample are special cases. The results of maximum likelihood and parametric bootstrap techniques are also proposed. Numerical example is presented for illustrative purposes. Results from simulation studies assessing the performance of our proposed method are included.