Edward Furman
Abstract
In this note we are concerned with the sums S=Y1+Y2+...+Yn, where every constituent follows the negative binomial distribution with arbitrary parameters. We derive the exact probability mass function and the cumulative probability function of S. We also show that one can relate to the distribution of S as a mixture negative binomial distribution.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
In this note we are concerned with the sums S=Y1+Y2+...+Yn, where every constituent follows the negative binomial distribution with arbitrary parameters. We derive the exact probability mass function and the cumulative probability function of S. We also show that one can relate to the distribution of S as a mixture negative binomial distribution.
Key concepts: Negative binomial distribution, Mathematics, Beta negative binomial distribution, Cumulative distribution function, Probability mass function, Binomial (polynomial), Binomial distribution, Beta-binomial distribution