Rare, outlier and extreme: beyond the Gaussian model and measures

Probability models for rare, outlier and extreme outcomes are different than the Gaussian (normal) distribution commonly used in management research. This paper illustrates the theoretical basis and implementation of these concepts. One example uses data on organisational size and compensation of CEOs in large US corporations in order to illustrate rare and outlier outcomes. Models that fit the data on these variables are very different than the Gaussian distribution, so mean, standard deviation and correlation are useless here. Another example uses data collected from business executives' economic forecasts shortly after the 9/11 terrorist attacks to illustrate how to identify extreme outcomes and a Bayesian approach for inferring relationship between extreme outcomes and strategy type. Differentiations between extremes and rares are illustrated using data simulated by a Monte Carlo method. Visualisation of fit of a model for data by Q-Q plot and discussion of distributional testing precedes some concluding remarks.