Application of Two Gamma Distributions Mixture to Financial Auditing

Abstract

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.

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Funding

The project is supported by the grant of the National Science Centre, Poland, DEC-2012/07/B/HS4/03073.

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Correspondence to Janusz L. Wywiał.

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Wywiał, J.L. Application of Two Gamma Distributions Mixture to Financial Auditing. Sankhya B 80, 1–18 (2018). https://doi.org/10.1007/s13571-018-0154-5

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• DOI: https://doi.org/10.1007/s13571-018-0154-5

Keywords and phrases

• Statistical auditing
• Accounting error
• Mixture of probability distribution
• Method of moments
• Likelihood ratio test

AMS (2000) subject classification

• Primary: 62H15
• Secondary: 91B28