Add probability mass functions

This function allows the addition of probability mass functions (PMFs) to produce a new PMF. This is useful for example in the context of reporting delays where the PMF of the sum of two Poisson distributions is the convolution of the PMFs.

Usage

add_pmfs(pmfs)

Arguments

pmfs

A list of vectors describing the probability mass functions to

Value

A vector describing the probability mass function of the sum of the

Details

This code was adapted from code written (under an MIT license) as part of the epinowcast package (https://github.com/epinowcast/epinowcast)

Examples

# Sample and analytical PMFs for two Poisson distributions
x <- rpois(10000, 5)
xpmf <- dpois(0:20, 5)
y <- rpois(10000, 7)
ypmf <- dpois(0:20, 7)
# Add sampled Poisson distributions up to get combined distribution
z <- x + y
# Analytical convolution of PMFs
conv_pmf <- add_pmfs(list(xpmf, ypmf))
conv_cdf <- cumsum(conv_pmf)
# Empirical convolution of PMFs
cdf <- ecdf(z)(0:42)
# Compare sampled and analytical CDFs
plot(conv_cdf)
lines(cdf, col = "black")