- Autor
- Sitek Grzegorz (University of Economics in Katowice, Poland)
- Tytuł
- Sum of Gamma and Normal Distribution
- Źródło
- Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska, 2020, z. 143, s. 275-284, bibliogr. 17 poz.
- Tytuł własny numeru
- Contemporary Management
- Słowa kluczowe
- Rachunkowość finansowa, Momenty rozkładu gamma, Dystrybucja
Financial accounting, Moments of gamma distribution, Distribution - Uwagi
- summ.
- Abstrakt
- Purpose: The article shows how to model audit errors using mixtures of probability distribution. Design/methodology/approach: In financial accounting, data about the economic activities of a given firm is collected and then summarized and reported in the form of financial statements. Auditing, on the other hand, is the independent verification of the fairness of these financial statements. An item in an audit sample produces two pieces of information: the book (recorded) amount and the audited (correct) amount. The difference between the two is called the error amount. The book amounts are treated as values of a random variable whose distribution is a mixture of the distributions of the correct amount and the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non-zero errors amounts. Findings: The sum of normal and gamma distribution can be useful for modeling audit errors. Originality/value: In this paper, the method of moments is proposed to estimate mixtures of probability distribution, and we derive a formulation of the probability distribution of the sum of a normally distributed random variable and one with gamma distribution. This research could be useful in financial auditing. (original abstract)
- Pełny tekst
- Pokaż
- Bibliografia
-
- Anderson, R.J. and Teitlebaum, A.D. (1973). Dollar-unit Sampling. Canadian Chartered Accountant, April, 30-39.
- Arkin, H. (1984). Handbook of Sampling for Auditing and Accounting. New York: McGraw Hill.
- Carr, P., Madan D.B. (2009). Saddlepoint Methods for Option Pricing. The Journal of Computational Finance, 13, 1, 49-61.
- Cyert, R.M., Hinckley, G.M., Monteverde, R.J. (1960). Statistical Sampling in the Audit of the Air Force Motor Vehicle Inventory. The Accounting Review, 35, 667-673.
- Deming, D.W. (1960). Sampling Design in Business Research. New York: Wiley.
- Golubev, A. (2010). Exponentially modified Gaussian (EMG) relevance to distributions related to cell proliferation and differentiation. Journal of Theoretical Biology, 262(2). doi: org/10.1016/j.jtbi.2009.10.005.
- Greene, W.H. (1990). A gamma-distributed stochastic fronier model. Journal of Econometrics, 46. North-Holland, 141-163.
- Grushka, E. (1972). Characterization of Exponentially Modified Gaussian Peaks in Chromatography. Analytical Chemistry. 44(11), 1733-1738.
- Hansen, M.H., Hurwitz, W.N. (1943). On the Theory of Sampling from Finite Populations. Annals of Mathematical Statistics, 14, 332-362.
- Johnson, J.R., Leitch, R.A., Neter, J. (1981). Characteristics of Errors in Accounts Receivables and Inventory Audits. Accounting Review, 58, 270-293.
- McLachlan, G., Peel, D. (2000). Finite Mixture Models. New York:Wiley.
- Plancade, S., Rozenholc, Y., Lund, E. (2012). Generalization of the normal- exponential model: exploration of a more accurate parameterisation for the signal distribution on Illumina BeadArrays. BMC Bioinformatics, 13(329). doi.org/10.1186/1471-2105-13-329.
- Roberts, D. (1978). Statistical Auditing. New York: American Institute of Certified Public Accountants.
- Silver, J. (2009). Microarray background correction: maximum likelihood estimation for the normal-exponential convolution model. Biostatistics, 10(2), 352-363.
- Stringer, K.W. (1963). Practical Aspects of Statistical Auditing. Preceeding of Business and Economic Statistics Section of the American Statistical Association, 405-41.
- Wywiał, J.L. (2016). Contributions to Testing Statistical Hypotheses in Auditing. Warsaw: PWN, 91-95.
- Wywiał, J.L. (2018). Application of two gamma distributions mixture to financial auditing. Sankhyã, B. The Indian Journal of Statistics. doi: org/10.1007/s13571-018-0154-5.
- Cytowane przez
- ISSN
- 1641-3466
- Język
- eng
- URI / DOI
- http://dx.doi.org/10.29119/1641-3466.2020.143.22
