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The relationship between two set of ranks can be evaluated by several coefficient of rank-order association. To judge the significance of an observed value of one of these statistics we need a reliable procedure for determining the $p$-value of the test. In several works the $t$-Student has been suggested as being relevant for the description of the null distribution of many coefficients. In this article, we propose a new model of density function, the generalized Gaussian on a finite range, which can be used to model data exhibiting a symmetrical unimodal density with a bounded domain. Several simulations illustrate the advantages of this technique over conventional methods. This is particularly useful in the case the number of ranks is larger than the threshold for which the exact null distribution is known, but lower than the threshold for which the asymptotic Gaussian approximation becomes valid.

A Model to Approximate the Distribution of Rank Order Associations