Comparing the Efficiency of Sample Plans for Symmetric and Non-symmetric Distributions in Auditing

The aim of the sampling in auditing fields is to produce an upper confidence limits for mean or totals of unobserved mistakes on the observed values accounts (called book values) that are highly positively skewed. In the main auditing scenarios, it is possible to meet populations with a relatively large number of small accounts combined with high rate of mistakes, that means diffused low errors, or populations with a relatively large number of accounts combined with a small rate of mistakes, that means rare high errors. It seems interesting to evaluate whether the sampling method in relation to the different distribution shape of the population is able to distinguish the pure random error from the systematic error. In this work we will compare, by simulation, the mostly used audit sampling methods for different distribution shapes for book values with different hypothesis on the presence of the errors on the book values population.