Negative Hypergeometric Distribution

Negative hypergeometric distribution, also known as the inverse hypergeometric or hypergeometric waiting-time distribution, is of interest in applications of inverse sampling without replacement from a finite population where a binary observation is made on each sampling unit. For example, imagine that a credit card company estimates that 18 of its 583 platinum card holders have gained their wealth illegally. A banking regulator is to perform an audit. “How many randomly selected platinum card holders will they have to investigate before finding a criminal?” It should be used in any situation where there is hypergeometric sampling and one is asking the question, “How many failures will I observe before I get s successes?” or alternatively “How many samples do I need to have s successes?” Sampling ...

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