The distributions of products and ratios of random variables are
of interest in many areas of the sciences. In this paper, the
exact distributions of the product <mml:math alttext="$| XY |$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math> and the ratio <mml:math alttext="$| X/Y|$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mrow><mml:mi>X</mml:mi><mml:mo>/</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math> are derived when <mml:math alttext="$X$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> and <mml:math alttext="$Y$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> are Laplace and Bessel function
random variables distributed independently of each other.

Journal of Applied Mathematics

On the product and ratio of Laplace and Bessel random variables

Abstract

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