Relationships Between the Negative Binomial and Negative Hypergeometric Distributions, with Applications to Testing and Estimation

SYNOPTIC ABSTRACT

A relation between the negative binomial and the negative hypergeometric distributions based on conditional distributions is proved. This relation allows to compute the critical value of an UMPU level a test concerning the comparison of probabilities of success in the one-sided case based on observed waiting times and to determine a UMVU estimator of the density of a negative binomial distribution in terms of a negative hypergeometric distribution. Moreover, some aspects of renewal theory are discussed.

Key Words and Phrases:

• negative binomial and negative hypergeometric distribution
• UMVU estimator
• UMPU level α test
• renewal theory