Abstract:

By using Bayesian method to analyze a class of (a,b) distribution, we studied the relationship between variance and expectation, and gave the moments estimation and maximum likelihood estimation (MLE) of a and b. Base on the MLE , we gave the Bayesian estimation of the classes distribution (a,b,0) by using Lindley approximation lemma, and used MATLAB to carry on the related simulation. Simulation results show that the choice of the Bayesian estimation is better if the sample size of (a,b,0) distribution estimation is large; conversely, the moment estimation is better.

Key words: class distribution, Bayesian estimation, moment estimation, maximum likelihood estimation (MLE), expectation, variance