Journal of Data Science

Abstract: Auditors are often faced with reviewing a sample drawn from special populations. One is the special population where invoices are divided into two categories, according to whether or not invoices are qualified. In other words, the qualified amount follows a nonstandard mixture distribution in which the qualified amount is either zero with a certain probability or the same as the known invoice amount with a certain probability. The other is the population where some invoices are partially qualified. In other words, some invoices have a qualified amount between zero and the full invoice amount. For these settings, the typical sample design is stratified random, with the estimation method employing a ratio type method. This paper focuses on efficient sample design for this setting and provides some guidelines in setting up stratum boundaries, calculating sample size and allocating sample size optimally across strata.