The Bayesian shrinkage estimation using progressive censoring sampling has acquired significant consideration among researchers in the recent decade. In this paper, we have introduced the Bayesian shrinkage estimation for the Erlang distribution by using Type-II progressive censored data. It is observed that the results of Bayesian shrinkage estimation are more tractable than Bayesian estimation and maximum likelihood estimation especially when prior information about the parameter is known in the form of point guess value. For comparison purposes, we have obtained Bayes estimate, Bayes shrinkage estimate, and maximum likelihood estimate along with their associated risks using generalized entropy loss function. The method of elicitation is also employed by using prior predictive distribution to calculate the values of hyperparameters. Some simulated comparisons of the estimates are presented here. Real-life data and rigorous simulation schemes are used to calculate Bayes estimates.
Mathematics Subject Classification: 62F10; 62F15; 62N02; 62N05