Computing Probability Density Functions of Compound Distributions: A Comparative Investigation

Abstract

The problem of evaluating compound probability distributions where one of the involved distributions is normal, frequently occurring when modelling communication channels in indoor industrial environments, is considered. Three different methods are investigated. They will here be named Gauss Newton Raphson (GNR), based on the Laplace approximation, Gauss- Hermite Quadratures (GHQ), and a Discrete Convolutional Sum (DCS). These three methods are investigated and compared for a one point problem assuming data that are continuous in amplitude, and a problem where data are assumed to be received in quantized bins. The relative integral approximation error, resulting from computing the compound distribution, is evaluated for the different methods and their complexities are compared. Simulations are provided to illustrate the advantages and disadvantages of the different methods.