New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications

Fitting a suitable distribution to the data from a real experiment is a crucial topic in statistics. However, many of the existing distributions cannot account for the effect of environmental conditions on the components under test. Moreover, the components are usually heterogeneous, meaning that they do not share the same distribution. In this article, we aim to obtain a new generalization of the Compound Rayleigh distribution by using mixture models and incorporating the environmental conditions on the components. The new distribution is expected to be a flexible distribution that encompasses some other distributions as special cases. We will also examine the properties and aging criteria of the new distribution. Over the past decades, various methods to estimate the unknown parameters of a statistical distribution have been proposed from the availability of type-II censored data. Thus, we estimate the parameters of the proposed distribution in the presence of type-II censored data using a Monte Carlo simulation study and real data analysis with maximum likelihood, maximum product of spacings, and Bayesian methods. Finally, different methods are compared by calculating the mean square error (MSE) of the resulting estimators.