Convert beta mean and precision parameters to two shape parameters

betaGetShapes(mean, precision)

Arguments

mean: The mean of a beta distribution
precision: The precision parameter (phi) of a beta distribution

Value

A list that includes the shape parameters of the beta distribution

Details

In simstudy, users specify the beta distribution as a function of two parameters - a mean and precision, where 0 < mean < 1 and precision > 0. In this case, the variance of the specified distribution is (mean)*(1-mean)/(1+precision). The base R function rbeta uses the two shape parameters to specify the beta distribution. This function converts the mean and precision into the shape1 and shape2 parameters.

Examples

set.seed(12345)
mean <- 0.3
precision <- 1.6
rs <- betaGetShapes(mean, precision)
c(rs$shape1, rs$shape2)
#> [1] 0.48 1.12
vec <- rbeta(1000, shape1 = rs$shape1, shape2 = rs$shape2)
(estMoments <- c(mean(vec), var(vec)))
#> [1] 0.30928690 0.08244181
(theoryMoments <- c(mean, mean * (1 - mean) / (1 + precision)))
#> [1] 0.30000000 0.08076923
(theoryMoments <- with(rs, c(
  shape1 / (shape1 + shape2),
  (shape1 * shape2) / ((shape1 + shape2)^2 * (1 + shape1 + shape2))
)))
#> [1] 0.30000000 0.08076923