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Application of Two Gamma Distributions Mixture to Financial Auditing

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  • Janusz L. Wywiał

    (University of Economics in Katowice)

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.

Suggested Citation

  • Janusz L. Wywiał, 2018. "Application of Two Gamma Distributions Mixture to Financial Auditing," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 1-18, May.
    • Handle: RePEc:spr:sankhb:v:80:y:2018:i:1:d:10.1007_s13571-018-0154-5
    DOI: 10.1007/s13571-018-0154-5
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    References listed on IDEAS

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    1. Frost, Pa & Tamura, H, 1986. "Accuracy Of Auxiliary Information Interval Estimation In Statistical Auditing," Journal of Accounting Research, Wiley Blackwell, vol. 24(1), pages 57-75.
    2. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Paper 1127, Economics Department, Queen's University.
    3. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    4. Kvanli, Alan H & Shen, Yaung Kaung & Deng, Lih Yuan, 1998. "Construction of Confidence Intervals for the Mean of a Population Containing Many Zero Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 362-368, July.
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    Cited by:

    1. Janusz L. Wywiał, 2020. "Estimating the population mean using a continuous sampling design dependent on an auxiliary variable," Statistics in Transition New Series, Polish Statistical Association, vol. 21(5), pages 1-16, December.
    2. Mingxing He & Jiahua Chen, 2022. "Consistency of the MLE under a two-parameter Gamma mixture model with a structural shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 951-975, November.

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