SOME IMPORTANT STATISTICAL PROPERTIES, INFORMATION MEASURES AND ESTIMATIONS OF SIZE BIASED GENERALIZED GAMMA DISTRIBUTION
Keywords:
Size Biased Generalized Gamma Distribution, Shannon’s Entropy, Generalized Entropy, Fisher’s Information Matrix, Likelihood Ratio Test, Maximum Likelihood Estimator.Abstract
In this paper, a new class of Size-biased Generalized Gamma (SBGG) distribution is defined. A Size-biased Generalized Gamma (SBGG) distribution, a particular case of weighted Generalized Gamma distribution, taking the weights as the variate values has been defined. The important statistical properties including hazard functions, reverse hazard functions, mode, moment generating function, characteristic function, Shannon’s entropy, generalized entropy and Fisher’s information matrix of the new model have been derived and studied. Here, we also study SBGG entropy estimation, Akaike and Bayesian information criterion. A likelihood ratio test for size-biasedness is conducted. The estimation of parameters is obtained by employing the classical methods of estimation especially method of moments and maximum likelihood estimator.
Downloads
References
Ahmed, A., Mir, K.A. and Reshi, J. A. (2013a). On new method of
estimation of parameters of Size-biased Generalized Gamma Distribution
and its Structural properties, IOSR Journal of Mathematics, Volume 5(2), p.
-40.
Ahmed, A, Reshi, J. A and Mir, K. A. (2013b). Structural properties of Size-
biased Gamma Distribution, IOSR Journal of Mathematics, 5(2), p. 55-61.
Akaike, H. (1973). Information Theory as an extension of the maximum
likelihood principle, Second International Symposium on Information
Theory, Akademiai Kiado, Budapest.
Akaike, H. (1974). A new look at the statistical model identification, IEEE
Transactions on Automatic Control, 19(6), p. 7-16.
Golan, Amos. (2006). A Review and synthesis, foundations and trends in
Econometrics, Information and Entropy measures, 2, p. 1-2.
Huang, P. H. and Hwang, T. Y. (2006). On new moment estimation of
parameters of the generalized gamma distribution using it’s characterization,
Taiwanese Journal of Mathematics, Volume 10(4), p. 1083-1093.
James Shannon C.E. (1948). A Mathematical theory of communication, Bell
system Technical Journal, 27, p. 623-659.
Kapur, J. N. (1989). Maximum Entropy Models in Science and Engineering,
Wiley, New York.
Mir, K.A, Ahmed, A. and Reshi, J. A. (2013). On Size-biased Exponential
Distribution, Journal of Modern Mathematics and Statistics,7 (2), p. 21-25.
Prentice, R. L. (1974). A Log gamma model and its maximum likelihood
estimation, Biometrika, 61, p.539-544.
Reshi, J. A., Ahmed, A. and Mir, K. A. (2014). On new moment method of
estimation of parameters of size-biased classical gamma distribution and its
characterization, International Journal of Modern Mathematical Sciences,
(2), p. 179-190.
Reshi, J. A., Ahmed, A. and Mir, K. A. (2014). Bayesain estimation of size
biased classical gamma distribution, Journal of Reliability and Statistical
Studies, 7(1), p. 31-42.
