Computation of Shot-Noise Probability Distributions and Densities

The computation of the cumulative distribution (cdf), the complementary cdf (ccdf), and the density of certain shot-noise random variables is discussed. After subtracting off a few terms that can be computed in closed form, what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a Fourier series whose coefficients are modulated samples of their characteristic function. To approximate the density, a spline is fit to the cdf samples and then differentiated. When the density has corners, it is important that the spline have coincident knots at these locations. For shot-noise densities, these locations are easily identified.