Statistical String Theory for Courts: If the Data Don't Fit . . . .

Abstract

The primary purpose of this article is to provide courts with an important new tool for applying the correct probability distribution to a given legal question. In areas as diverse as criminal prosecutions and civil lawsuits alleging securities fraud, courts must assess the relevance and reliability of data and the inferences drawn therefrom. But, courts and ex-pert witnesses often make mistaken assumptions about what probability distributions are appropriate for their analyses. Using the wrong probability distribution can lead to invalid factual conclusions and unjustified legal outcomes. To deal with this problem, we propose the use of a unifying statistical string theory - the g-and-h distribution - in legal settings. This parent distribution subsumes many other distributions and spans the widest range of possible skewness-kurtosis combinations. The capacity of the g-and-h distribution to accommodate such a wide variety of data can alleviate judicial fact finders of the difficult task of trying to correctly select among competing distributions. Finally, we report the successful use of this tool in a trial setting for financial data analysis - showing that it can produce more accurate inferences, than those drawn from alternative distributions, and these differences can be judicially decisive.