Based on the record samples, the empirical Bayes estimators of parameter and reliability function for Compound Rayleigh distribution is investigated under the symmetric and asymmetric loss function. In this case the symmetric loss function is squared error and for the asymmetric loss functions, we consider LINEX and general Entropy loss function. In this paper, we obtain the Bayes estimators of the parameter and reliability function Different from the predecessor, the empirical Bayes estimators of the parameter and reliability function are then derived where hyper-parameter is estimated using maximum likelihood method. In order to investigate the accuracy of the estimation methods, an illustrative example is examined numerically by means of Monte-Carlo simulation.

Over the past decades, various methods to estimate the unknown parameter, the survival function, and the hazard rate of a statistical distribution have been proposed from the availability of type-II censored data. They are all differing in terms of how the progressive type-II censored data of the underlying distribution are available. In this study, we estimate the parameter, the survival function, and the hazard rate of the compound Rayleigh distribution by using the E-Bayesian estimation when the progressive type-II censored data are available. The resulting estimators are evaluated based on the asymmetric general entropy and the symmetric squared error loss functions. In addition, the E-Bayesian estimators under the different loss functions have been compared through a real data analysis and Monte Carlo simulation studies by calculating the E-MSE of the resulting estimators.

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Most of the real-life populations are heterogeneous and homogeneity is often just a simplifying assumption for the relevant statistical analysis. Mixtures of lifetime distributions that correspond to homogeneous subpopulations were intensively studied in the literature. Various distributional and stochastic properties of finite and continuous mixtures were discussed. In this paper, following recent publications, we develop further a mixture concept in the form of the generalized α-mixtures that include all mixture models that are widely explored in the literature. We study some main stochastic properties of the suggested mixture model, that is, aging and appropriate stochastic comparisons. Some relevant examples and counterexamples are given to illustrate our findings.