Frequency Distributions

This chapter reviews distributions that can be used to model the frequency of operational losses, focusing on the Poisson counting process and its variants. The geometric distribution is useful to model the probability that an event occurs for the first time, given that it has not occurred before. The main difference between the Poisson distribution and the binomial distribution is that the former does not make an assumption regarding the total number of trials. The Poisson distribution is used to find the probability that a certain number of events would arrive within a fixed time interval. The plot should roughly look like a straight horizontal line, centered around the mean. If the plot is steadily increasing, decreasing, or significantly oscillating, this may indicate that the assumption of a constant intensity rate is not valid, and alternative models should be sought. A chaotic behavior of the intensity rate may be captured by a random stochastic process, such as Brownian motion.