Correlation

Actuaries frequently are called upon to estimate sums of random variables. Such sums arise in a variety of contexts, as aggregate loss distributions, as losses including loss adjustment expense, as losses to a particular layer in stop loss reinsurance. If the quantities being summed were independent, things would be easy, however this is seldom the case. Generally, there will be some amount of "correlation" between the summands. This paper examines the Pearson product moment correlation coefficient's strengths and weaknesses and discusses two non-parametric alternatives: the Spearman rank correlation coefficient and Kendall's tau statistic.