dVIB | R Documentation |
The function computes the probability density function of the variance-inflated beta distribution. It can also compute the probability density function of the augmented variance-inflated beta distribution by assigning positive probabilities to zero and one and a (continuous) variance-inflated beta density to the interval (0,1).
dVIB(x, mu, phi, p, k, q0 = NULL, q1 = NULL)
x |
a vector of quantiles. |
mu |
the mean parameter of the variance-inflated beta distribution. It must lie in (0, 1). |
phi |
the precision parameter of the variance-Inflated distribution. It must be a positive real value. |
p |
the mixing weight. It must lie in (0, 1). |
k |
the extent of the variance inflation. It must lie in (0, 1). |
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 VIB distribution is a special mixture of two beta distributions with density
f_{VIB}(x;μ,φ,p,k)=p f_B(x;μ,φ k)+(1-p)f_B(x;μ,φ)
for 0<x<1, where f_B(x;\cdot,\cdot) is the beta density with a mean-precision parameterization. Moreover, 0<p<1 is the mixing weight, 0<μ<1 represents the overall (as well as mixture component) mean, φ>0 is a precision parameter, and 0<k<1 determines the extent of the variance inflation. The augmented VIB distribution has density
q_0, if x=0
q_1, if x=1
(1-q_0-q_1)f_{VIB}(x;μ,φ,p,k), 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
.
Di Brisco, A. M., Migliorati, S., Ongaro, A. (2020). Robustness against outliers: A new variance inflated regression model for proportions. Statistical Modelling, 20(3), 274–309. doi:10.1177/1471082X18821213
dVIB(x = c(.5,.7,.8), mu = .3, phi = 20, p = .5, k= .5) dVIB(x = c(.5,.7,.8), mu = .3, phi = 20, p = .5, k= .5, q1 = .1) dVIB(x = c(.5,.7,.8), mu = .3, phi = 20, p = .5, k= .5, q0 = .2, q1 = .1)
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