# dVIB: Variance-inflated beta probability density function In FlexReg: Regression Models for Bounded Responses

## Description

The function computes the probability density function of the variance-inflated beta distribution.

## Usage

 1 dVIB(x, mu, phi, p, k) 

## Arguments

 x a vector of quantiles. mu the mean parameter. It must lie in (0, 1). phi the precision parameter. 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).

## Details

The VIB distribution is a special mixture of two beta distributions

p Beta(x|μ,φ k)+(1-p)Beta(x|μ,φ)

for 0<x<1 where Beta(x|\cdot,\cdot) is the beta distribution 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.

## Value

A vector with the same length as x.

## References

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

## Examples

 1 dVIB(x = c(.5,.7,.8), mu = 0.3, phi = 20, p = .5, k= .5) 

FlexReg documentation built on Jan. 17, 2022, 5:06 p.m.