Description Usage Arguments Details Value References Examples

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

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

`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). |

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.

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

1 |

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