On compounded geometric distributions and their applications

ABSTRACT

Here, we introduce two-parameter compounded geometric distributions with monotone failure rates. These distributions are derived by compounding geometric distribution and zero-truncated Poisson distribution. Some statistical and reliability properties of the distributions are investigated. Parameters of the proposed distributions are estimated by the maximum likelihood method as well as through the minimum distance method of estimation. Performance of the estimates by both the methods of estimation is compared based on Monte Carlo simulations. An illustration with Air Crash casualties demonstrates that the distributions can be considered as a suitable model under several real situations.

KEYWORDS:

• Compounding
• Hazard rate function
• Markov chain Monte Carlo
• Maximum likelihood estimation
• Method of minimum distance
• Zero-truncated Poisson distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62E99
• Secondary 62N05
• 62F10

Acknowledgments

Authors are grateful to Mr. Richard Kebabjian, owner of the website www.planecrashinfo.com for his kind permission to access the data. The suggestions and comments by the editor, the associate editor, and the reviewers are acknowledged gratefully by the authors. The financial support from NBHM, DAE, Government of India (Grant No. 2/48(25)/2014/NBHM (R.P.) R&D II/1393 dated 3.2.2015) is gratefully acknowledged by Asok K. Nanda.