Statistical aspects of Tricomi's function and modified Bessel functions of the second kind (Q1584578)

In this paper it is shown that modified Bessel functions of the second kind \(K_\nu(x)\) and Tricomi's confluent hypergeometric function \(U(a,b,t)\) arise in products of independent random variables which lead to statistical methods of simulating their values and the cumulative distribution functions of the two exponential class distributions based on them. The moment solutions found here for the parameters ot the Halphen distributions and the exponential distribution based on Tricomi's function offer a quick and simple indication of the suitability of the data before undertaking the maximum likelihood solution. In addition simulation offers an alternative to numerical integration for estimating the cumulative distribution function of the two distributions. Tricomi's exponential distribution can be used to add a very flexible member to the class of discrete distributions with hypergeometric probabilities.