The function computes the probability density function of the beta distribution with a mean-precision parameterization.
Usage
dBeta_mu(x, mu, phi)
Value
A vector with the same length as x.
Arguments
x
a vector of quantiles.
mu
the mean parameter. It must lie in (0, 1).
phi
the precision parameter. It must be a positive real value.
Details
The beta distribution has density
$$\frac{\Gamma{(\phi)}}{\Gamma{(\mu\phi)}\Gamma{((1-\mu)\phi)}}x^{\mu\phi-1}(1-x)^{(1-\mu)\phi-1}$$
for \(0<x<1\), where \(0<\mu<1\) identifies the mean and \(\phi>0\) is the precision parameter.
References
Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799--815. doi:10.1080/0266476042000214501