# Probability density function of the flexible beta distribution The function computes the probability density function of the flexible beta distribution. It can also compute the probability density function of the augmented flexible beta distribution by assigning positive probabilities to zero and/or one values and a (continuous) flexible beta density to the interval (0,1). ```r dFB(x, mu, phi, p, w, 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). - `w`: the normalized distance among component means. 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 FB distribution is a special mixture of two beta distributions with probability density function $$ f_{FB}(x;\mu,\phi,p,w)=p f_B(x;\lambda_1,\phi)+(1-p)f_B(x;\lambda_2,\phi), $$ for $00$ is a precision parameter, $0

dFB function