dBeta function

Probability density function of the beta distribution

The function computes the probability density function of the beta distribution with a mean-precision parameterization. It can also compute the probability density function of the augmented beta distribution by assigning positive probabilities to zero and/or one values and a (continuous) beta density to the interval (0,1).

dBeta(x, mu, phi, q0 = NULL, q1 = NULL)

Arguments

• x: a vector of quantiles.
• mu: the mean parameter. It must lie in (0, 1).
• phi: the precision parameter. It must be a real positive value.
• q0: the probability of augmentation in zero. It must lie in (0, 1). In case of no augmentation, it is NULL (default).
• q1: the probability of augmentation in one. It must lie in (0, 1). In case of no augmentation, it is NULL (default).

Returns

A vector with the same length as x.

Details

The beta distribution has density

for $0<x<1$, where $0<\mu<1$ identifies the mean and $\phi>0$ is the precision parameter.

The augmented beta distribution has density

• $q_0$, if $x=0$
• $q_1$, if $x=1$
• $(1-q_0-q_1)f_B(x;\mu,\phi)$, if $0\<x\<1$

where $0<q_0<1$ identifies the augmentation in zero, $0<q_1<1$ identifies the augmentation in one, and $q_0+q_1<1$.

Examples

dBeta(x = c(.5,.7,.8), mu = .3, phi = 20)
dBeta(x = c(.5,.7,.8), mu = .3, phi = 20, q0 = .2)
dBeta(x = c(.5,.7,.8), mu = .3, phi = 20, q0 = .2, q1= .1)

References

Ferrari, S.L.P., Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31 (7), 799--815. doi:10.1080/0266476042000214501