Exact distribution of the product and the quotient of two stable Lévy random variables

• The PDF of the product and the quotient of stable distributions have been obtained.
• The CDF of the product and the quotient of stable distributions have been obtained.
• A Mathematica algorithm has been written to evaluate the expressions developed.
• Numerical experiments are carried out to show the accuracy of the formulas derived.

In the present paper, the exact probability density function and cumulative distribution function of the product and the quotient of two independent stable Lévy random variables are derived in terms of the H-function. For practical applications, a routine in the Mathematica software has been developed for the evaluation of the H- function. Finally, numerical experiments are carried out to show the accuracy and correctness of the expressions hereby deduced.