An empirical investigation of analytical procedures using mixture distributions

摘要

Analytical procedures are evaluations of account and transaction flow information made by arnstudy of plausible relationships between both accounting and non‐accounting data. This studyrninvestigates the performance of Tweedie distributions (which have Gaussian distributions asrnmembers) in improving fit of zero‐inflated, non‐negative, kurtotic and multimodal analyticalrnreview data. The study found that account valuations are more informative than marginal datarnin analytical review, that mixture Poisson–Gamma distributions offer better fit than Gaussian distributions,rneven under assumptions of central limit theorem convergence, and that mixturernPoisson–Gamma distributions provide better predictions of future account and transaction volumesrnand values. Model performance improvement with price versus returns data in this empiricalrnstudy was substantial: from less than one‐quarter of variance, to almost two‐thirds. Tweedierngeneralized linear model risk assessments were found to be a magnitude smaller than traditionalrnrisk assessments, lending support to market inefficiency and increased risk from idiosyncratic factors.rnAn example with several differing distributions shows that use of mixture distributionsrninstead of point estimation can reduce sample size while retaining the power of the audit tests.rnThe results of this study are increasingly important as accounting datasets are growing exponentiallyrnlarger over time, requiring well‐defined roles for models, algorithms, data and narrativernwhich can only be achieved with statistical protocols and algorithmic languages.