SOME IMPORTANT STATISTICAL PROPERTIES, INFORMATION MEASURES AND ESTIMATIONS OF SIZE BIASED GENERALIZED GAMMA DISTRIBUTION

  • J. A. Reshi Department of Statistics, University of Kashmir, Srinagar, India.
  • A. Ahmed Department of Statistics & Operation Research, Aligarh Muslim University,India
  • K. A. Mir Department of Statistics, Govt. Degree College Bemina Srinagar, India.
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.

 

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Published
2014-11-12
Section
Articles