Prony approximations for probability density functions

Performance evaluation of many systems in radar, sonar, and communications is often hampered by the complicated, if not intractable, analytical form of an underlying probability density function (pdf). In this paper, we propose the use of the Prony method to generate an exponential sum approximation to the pdf of positive random variables. The Prony method is well-known in signal processing, yet has not been applied to this application. The Prony method reduces the problem of estimating the modes and mode amplitudes of an exponential sum to that of two least squares problems. We illustrate the efficiacy of the method on several examples in statistical communications theory