Description Usage Arguments Details Value Author(s) References See Also Examples

Density and random generation for the binomial distribution with optional dispersion parameter calculation.

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`k` |
number of simulations. |

`n` |
the maximum score of the binomial trials. |

`p` |
the probability of scoring a success in each binomial trial. |

`phi` |
the dispersion parameter of the binomial distribution. If |

The inclusion of a dispersion parameter in the variance equation of the binomial distribution relaxes the relationship that is expected between the mean and variance in binomial models,

*E[y]=np, \quad Var[y]=φ np(1-p).*

The density function of this binomial model is calculated considering as an exponential family, where the density function has the following form

*f(y)=\frac{y log(p/(1-p))+n log(1-p)}{φ}+c(y,φ),*

where *c(y,φ)* is a function that is approximated by the deviance of the model.

`dBI`

gives the density of a binomial distribution for those `n`

, `p`

and `phi`

parameters.

`rBI`

generates `k`

random observations based on a binomial distribution with those `n`

, `p`

and `phi`

parameters.

Josu Najera Zuloaga

Dae-Jin Lee

Pawitan Y. (2001): In All Likelihood: Statistical Modelling and Inference Using Likelihood, *Oxford University Press.*

The `rbinom`

function of package `<stats>`

. This function performs simulations based on a binomial distribution without dispersion parameter.

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