Incorporating an Integral equation for characteristic functions in investigating a class of distributions

Abstract

Integral equations of characteristic functions are very strong analytical tools for investigating the distributions of stochastic models. The paper makes use of an integral equation, incorporating the characteristic function of a renewal distribution and the characteristic function of a uniform random contraction, for establishing a characterization of a class of selfdecomposable distributions. Moreover, the paper establishes interpretations in stochastic modeling of risk severity reduction operations of the uniform random contraction and the characterization of that class of selfdecomposable distributions.

Keywords:

• Integral equation
• Random contraction
• Characteristic function