ACST3060: Discrete Convolutions in R

Week 5 content (2024) for ACST3060 and ACST8085 (Quantitative Methods for Risk Analysis). We create, in R, functions to derive the distribution of discrete convolutions. More specifically:
• The first function (which we call “convo”) can be used to find the probability mass function (PMF) of a convolution “S=X1+X2”, where X1 and X2 are discrete random variables (possibly with different distributions) taking values on a set of non-negative integers.
• The second function (which we call “convo.n”) can be used to find the PMF of a convolution “S=X1+X2+...+X_n”, where X1, X2,...Xn, all have the same discrete distribution (taking values on a set of non-negative integers).
(Narrated by Dr Guillaume Boglioni)