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

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

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.