Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-29T00:33:51.673Z Has data issue: false hasContentIssue false

THEORETICAL PROPERTIES OF THE WEIGHTED GENERALIZED GAMMA AND RELATED DISTRIBUTIONS

Published online by Cambridge University Press:  21 April 2015

Hewa A. Priyadarshani
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634USA
Broderick O. Oluyede
Affiliation:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460USA E-mail: boluyede@georgiasouthern.edu

Abstract

A new class of weighted generalized gamma distribution (WGGD) and related distributions are presented. Theoretical properties of the generalized gamma model, WGGD including the hazard function, reverse hazard function, moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, and entropy measures are derived. The results presented here generalizes the generalized gamma distribution and includes several distributions as special cases. The special cases include generalized gamma, weighted gamma, weighted exponential, weighted Weibull, weighted Rayleigh distributions, and their underlying or parent distributions.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ali, M.M., Woo, J. & Nadarajah, S. (2008). Generalized gamma variables with drought application. Journal of the Korean Statistical Society 37: 3745.Google Scholar
2. Finkelstein, M.S. (2002). On the reverse hazard rate. Reliability Engineering and System Safety 78: 7175.Google Scholar
3. Fisher, R.A. (1934). The effects of methods of ascertainment upon the estimation of the frequencies. Annals of Human Genetics 6(1): 439444.Google Scholar
4. Glaser, R.E. (1980). Bathtub and related failure rate characterizations. Journal of American Statistical Association 75: 667672.Google Scholar
5. Golan, A. (2009). Information and entropy in econometrics—a review and synthesis. Foundations and Trends in Econometrics 2(1–2): 1145.Google Scholar
6. Huang, P.H. & Hwang, T.Y. (2006). On new moment estimation of parameters of the generalized gamma distribution using its characterization. Taiwanese Journal of Mathematics 10(4): 10831093.Google Scholar
7. Khodabin, M. & Ahamadabadi, A. (2010). Some properties of generalized gamma distribution. Mathematical Sciences 4(1): 928.Google Scholar
8. Lehmann, E.L. (1998). Theory of point estimation. New York: Springer-Verlag.Google Scholar
9. Nadarajah, S. & Gupta, A.K. (2007). A generalized gamma distribution with application to drought data. Mathematics and Computers in Simulation 74: 17.Google Scholar
10. Patil, G.P. & Rao, C.R. (1977). Weighted distributions: a survey of their application. In Krishnaiah, P.R. (Ed.), Applications of Statistics North Holland Publishing Company, pp. 383405.Google Scholar
11. Patil, G.P. & Rao, C.R. (1978). Weighted distributions and size-biased sampling with applications to wildlife and human families. Biometrics 34: 179189.Google Scholar
12. Patil, G.P. & Ord, J.K. (1997). Weighted distributions. In Armitage, P. & Colton, T., (eds.), Encyclopedia of biostatistics, Vol. 6, Chichester: Wiley, pp. 47354738.Google Scholar
13. Renyi, A. (1961). On measures of entropy and information. In Proceedings of Fourth Berkley Symposium on Mathematical Statistics and Probability, 1960, Vol 1, Berkeley: University of California Press, pp. 547–561.Google Scholar
14. Rao, C.R. (1965). On discrete distributions arising out of methods of ascertainment, in classical and contagious discrete distributions. In (Patil, G.P., Ed.), Calcutta: Pergamon Press and Statistical Publishing Society, pp. 320–332.Google Scholar
15. Rao, C.R. (1985). Weighted distributions arising out of methods of ascertainment. In Atkinson, A.C. & Fienberg, S.E. (eds.), A Celebration of statistics, New York: Springer-Verlag, Chapter 24, pp. 543569.Google Scholar
16. Stacy, E.W. (1962). A generalization of the gamma distribution. The Annals of Mathematical Statistics 33(3): pp. 11871192.Google Scholar
17. Yaghoobi, M.A.R., Borzadaran, G.R.M. & Yari, G.H. (2010). β-entropy for Pareto-type distributions and related weighted distributions. Statistics & Probability Letters 80(19–20, 1–15): 15121519.Google Scholar