Title: Application of Two Gamma Distributions Mixture to Financial Auditing

Author(s): Janusz L. Wywial
Issue: Volume 80 Series B Part 1 Year 2018
Pages: 1 -- 18
The considered problem can be treated as a particular topic in the field of testing some substantive hypothesis in financial auditing. The main theme of the paper is the well-known problem of testing hypothesis on admissibility of the population total of accounting errors amounts. The set of items with non-zero errors amounts is the domain in the accounting population. The book amounts are treated as values of a random variable which distribution is a mixture of the distributions of correct amount and the distribution of the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non-zero errors amounts. The mixture of two gamma distributions is taken into account. The well-known method of moments and likelihood method are proposed to estimate parameters of distribution. It let us construct some statistic to test the outlined hypothesis. Moreover, the well-known likelihood ratio test is considered.
AMS (2000) subject classification. Primary: 62H15; Secondary: 91B28.
Keywords and phrases: Statistical auditing, Accounting error, Mixture of probability distribution, Method of moments, Likelihood ratio test