Mean parameterization the beta pdf.

Mean parameterization the beta pdf.

Usage

dbeta_mean(x, mu, phi, log = FALSE)

Arguments

x

x-value, x e (0, 1)

mu

Mean parameter, mu e (0, 1)

phi

Precision parameter, phi > 0

log

Optional argument. If TRUE, returns log(pdf). Normally False.

Value

PDF of custom Beta Distribution

Details

The Beta Distribution has Density $$f(y | \mu, \phi) = \frac{\Gamma(\phi) x^{\mu\phi - 1} (1 - x)^{(1-\mu)\phi}}{\Gamma(\mu\phi)\Gamma((1 - \mu)\phi)} $$

With parameterisation of the usual Beta-Distribution's shape parameters a and b as: $$a := \mu\phi, b := (1 - \mu)\phi$$

Examples

x <- seq(from = 0.01, to = 0.99, length.out = 1000)
plot(x, dbeta_mean(x, mu = 0.5, phi = 1), type = "l")