Downton’s bivariate exponential distribution has been a popular model for hydrological sciences. However, it seems that no explicit expressions for its product moments are available. In this short note, we provide a direct derivation of a general expression for the product moments and also...

Motivated by hydrological applications, we derive the exact distributions of R=X + Y, P=XY and W=X/(X+Y) and the corresponding moment properties when X and Y follow Friday and Patil's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska....

In this paper, we derive an exact test for a column of the covariance matrix. The test statistic is calculated by using a single observation. The exact distributions of the test statistic are derived under both the null and alternative hypotheses. We also obtain an analytical expression of the...