# Probability density function of the variance-inflated beta distribution 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/or one values and a (continuous) variance-inflated beta density to the interval (0,1). ```r dVIB(x, mu, phi, p, k, 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. - `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, 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 VIB distribution is a special mixture of two beta distributions with probability density function $$ f_{VIB}(x;\mu,\phi,p,k)=p f_B(x;\mu,\phi k)+(1-p)f_B(x;\mu,\phi), $$ for $00$ is a precision parameter, and $0

dVIB function