Multinomial-Dirichlet Bounds for Dollar-Unit Sampling in Auditing.

Abstract ABSTRACT: This paper takes a Bayesian approach to incorporate auditors' prior information in constructing error bounds for the proportion of dollar amount overstated (equivalently, the total amount overstated) in an accounting population. The multinomial distribution model within the dollar-unit sampling framework suggested by Fienberg, Neter, and Leitch 1977 is used, and the prior distribution belongs to the class of Dirichlet distributions. The properties of the resulting Bayesian bounds are discussed. Some comparisons of tightness of bounds are made with the multinomial and the modified multinomial bounds Leitch, et al., 1982. Simulation results suggest that some of the Bayesian bounds have good repeated sampling properties, in particular, in repeated sampling, a Bayesian bound gives a significance level close to the nominal level for many typical accounting populations. Another advantage of the suggested approach is computational efficiency which is independent of the sample size and the number of errors found in the sample.