Modeling loss exchange ratios as inverse Gaussian variates: Implications

Loss Exchange Ratios (LER) are widely used as the summary of the results of a simulated battle. We have found from repeated simulations of the same battle that the LER for a given battle varies widely. This has policy and statistical implications. Attacking some of the statistical issues, such as what is a good model for LER and how to estimate its parameters, sheds light on the policy issues, such as how many runs are required and how accurate is the output. We examine in detail LER from replications of battles simulated on JANUS and CASTFOREM, and propose a new statistical model for this output, based on the Inverse Gaussian distribution. Since this member of the exponential family is not widely known, we include a primer. We make the point that the LER can not be adequately summarized by just its mean; a second parameter is necessary to fully describe the model. Executives should routinely ask their modelers how many runs of a simulation were conducted in a simulation study, how that number was selected, how the LER (or other summary output) is best described, and how much improvement has been demonstrated over the controls. This article provides the analyst with powerful tools to answer those questions.