Parameterisation conversion for beta distribution

Get beta distribution's two shape parameters from mean value and variance.

Usage

get_beta_parameters(mu, sigmasq, a = 0, b = 0.5)

Arguments

mu

mean value

sigmasq

variance

a

lower support bound

b

upper support bound

Examples

a <- 2
b <- 6
m <- a / (a + b)
v <- (a*b)/((a+b)^2 * (a + b +1))
get_beta_parameters(m, v)
#> [1] 1 1
get_beta_parameters(1e-2, 1e-3)
#> [1] 0.078 3.822
# p <- get_beta_parameters(0.1, 0.01); curve(dbeta(x, p[1], p[2]), from = 0, to = 1)
# p <- get_beta_parameters(0.1, 0.001); curve(dbeta(x, p[1], p[2]), from = 0, to = 1)
# p <- get_beta_parameters(0.1, 0.0001); curve(dbeta(x, p[1], p[2]), from = 0, to = 1)

s12 <- get_beta_parameters(mu = 1e-2, sigmasq = 1e-3, a = 0, b = 0.5)
x <- rbeta05(1000, s12[1L], s12[2L])
mean(x); var(x)
#> [1] 0.01035644
#> [1] 0.001002918

s12 <- get_beta_parameters(mu = 1e-5, sigmasq = 1e-7, a = 0, b = 0.5)
x <- rbeta05(10000, s12[1L], s12[2L])
mean(x); var(x)
#> [1] 7.08732e-06
#> [1] 3.425107e-08