Estimation Based on Generalized Order Statistics from the Burr Model

ABSTRACT

The concept of generalized order statistics was introduced by Kamps (1995) to unify several concepts that have been used in statistics such as order statistics, record values, and sequential order statistics. Estimation of the parameters of the Burr type XII distribution are obtained based on generalized order statistics. The maximum likelihood and Bayes methods of estimation are used for this purposes. The Bayes estimates are derived by using the approximation form of Lindley (1980). Estimation based on upper records from the Burr model is obtained and compared by using Monte Carlo simulation study. Our results are specialized to the results of AL-Hussaini and Jaheen (1992) which are based on ordinary order statistics.

Key Words:

• Bayes estimation
• Burr model
• Generalized order statistics
• Monte Carlo simulation
• Record values

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62F15

Acknowledgments

The author wishes to thank anonymous referees for their comments which improved the article.