Convert negative binomial mean and dispersion parameters to size and prob parameters

negbinomGetSizeProb(mean, dispersion)

Arguments

mean: The mean of a gamma distribution
dispersion: The dispersion parameter of a gamma distribution

Value

A list that includes the size and prob parameters of the neg binom distribution

Details

In simstudy, users specify the negative binomial distribution as a function of two parameters - a mean and dispersion. In this case, the variance of the specified distribution is mean + (mean^2)*dispersion. The base R function rnbinom uses the size and prob parameters to specify the negative binomial distribution. This function converts the mean and dispersion into the size and probability parameters.

Examples

set.seed(12345)
mean <- 5
dispersion <- 0.5
sp <- negbinomGetSizeProb(mean, dispersion)
c(sp$size, sp$prob)
#> [1] 2.0000000 0.2857143
vec <- rnbinom(1000, size = sp$size, prob = sp$prob)
(estMoments <- c(mean(vec), var(vec)))
#> [1]  5.08500 18.87865
(theoryMoments <- c(mean, mean + mean^2 * dispersion))
#> [1]  5.0 17.5
(theoryMoments <- c(sp$size * (1 - sp$prob) / sp$prob, sp$size * (1 - sp$prob) / sp$prob^2))
#> [1]  5.0 17.5