Structural properties of size biased Gamma distribution

In this paper, a new class of size-biased Gamma distribution is derived. A size-biased gamma distribution, a particular case of weighted gamma distribution, taking the weights as the variate values has been defined. A new distribution which contains as a special case is introduced. The characterizing properties of the model are derived. A Baye's estimator of Size-biased gamma distribution (SBGMD) has also been obtained by using different priors. Also, other important properties including Shannon entropy and Fisher's information matrix which are the measure of the uncertainty in this class of the distribution are derived and studied.