Sum of gamma and normal distribution

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.