Consistent estimation of parameters and quantiles of the three-parameter gamma distribution based on Type-II right-censored data

Abstract

In this paper, we propose a method of estimation of parameters and quantiles of the three-parameter gamma distribution based on Type-II right-censored data. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs well compared with another prominent method of estimation in terms of bias and root mean-squared error in small-sample situations. Finally, two real data sets are used for illustrating the proposed method.

Keywords:

• gamma distribution
• maximum likelihood estimation
• consistency
• existence
• uniqueness
• bias
• mean-squared error
• Monte Carlo simulation

AMS Subject Classification::

• 62F10
• 62F86

Acknowledgements

The authors thank the editor, the associate editor and two referees for incisive comments and suggestions which led to a great improvement in the paper. Hideki Nagatsuka was partially supported by the Grant-in-Aid for Young Scientists (B) 24710170, The Ministry of Education, Culture, Sports, Science and Technology, Japan, which facilitated his collaborate research visit to the department of the second author.