Development of size-biased Mukherjee-Islam distribution

Abstract

In the present article, we derived a new Size-biased distribution from Mukherjee-Islam distribution. Flexibility of the model is derived by its moments, moment generating function (mgf) and characteristic function. Other important properties like Fisher's information matrix and Shannon's entropy are also derived which gives the measure of uncertainty in the system. Maximum likelihood estimator (MLE) and Baye's estimator of size-biased distribution are obtained and in the last, test of size biasedness is done.