A test for independence in a multivariate exponential distribution with equal correlation coefficients

A rank statistic is considered which may be used for testing for total independence in a p-variate exponential distribution with equal correlation coefficients. Critical values for the statistic are provided for p = 3.4 and sample sizes less than or equal to 20. Finally, the small sample power performance of the rank test relative to that of the locally most powerful similar lest under the exponential alternative is evaluated.