On Size-Biased Negative Binomial Distribution and its Use in Zero-Truncated Cases

A size-biased negative binomial distribution, a particular case of the weighted negative binomial distribution, taking the weights as the variate values has been defined. A Bayes' estimator of size-biased negative binomial distribution (SBNBD) has been obtained by using non-informative and gamma prior distributions. Also comparison has been made of this estimator with the corresponding maximum likelihood estimator (MLE) with the help of R- Software.