Application of the Hypergeometric Distribution In a Special Case of Rare Events

Auditors are often faced with reviewing a sample of business invoices and estimating the number of error items and the total error amount for a rarely occurring event. One special case is dividing the dollars in a large population of invoices into two categories according to whether they meet or do not meet the requirements, are or are not in error. In other words, the error amount follows a nonstandard mixture distribution in which the error amount is either zero with a large probability or the original invoice amount with a very small probability. It is likely that the sample or some strata of the sample will include only zero error items. Under this scenario, the classical method will not produce satisfactory estimation, especially when a conservative estimate of the number of error items or error amount is needed. We will show some flexible applications using the hypergeometric distribution.