An empirical investigation of analytical procedures using mixture distributions

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