dBeta_mu | R Documentation |
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 one and a (continuous) beta density to the interval (0,1).
dBeta_mu(x, mu, phi, q0 = NULL, q1 = NULL)
x |
a vector of quantiles. |
mu |
the mean parameter of the beta distribution. It must lie in (0, 1). |
phi |
the precision parameter of the Beta distribution. It must be a positive real value. |
q0 |
the probability of augmentation in zero. It must lie in (0, 1). In case of no augmentation is |
q1 |
the probability of augmentation in one. It must lie in (0, 1). In case of no augmentation is |
The beta distribution has density
f_B(x;μ,φ)=\frac{Γ{(φ)}}{Γ{(μφ)}Γ{((1-μ)φ)}}x^{μφ-1}(1-x)^{(1-μ)φ-1}
for 0<x<1, where 0<μ<1 identifies the mean and φ>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;μ,φ), 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.
A vector with the same length as x
.
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
dBeta_mu(x = c(.5,.7,.8), mu = .3, phi = 20) dBeta_mu(x = c(.5,.7,.8), mu = .3, phi = 20, q0 = .2) dBeta_mu(x = c(.5,.7,.8), mu = .3, phi = 20, q0 = .2, q1= .1)
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