On a new multivariate distribution and its properties

We define a new statistic U as a difference of two different variates which are both distributed in the form of Bessel functions of purely imaginary argument as obtained by Bhattacharya (1946). Then the principle of Characteristic functions and the method of operational calculus has been utilised to determine the probability distribution and sampling distribution of U. Though the distributions are some-what complex, their moments and cumulants indicate that they are symmetrical and leptokurtic in form and that they approximate to the normal distribution when the sample sizes are large.