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

View source: R/DoubleBinomial.R

The function `DBI()`

defines the double binomial distribution, a two parameters distribution, for a `gamlss.family`

object to be used in GAMLSS fitting using the function `gamlss()`

. The functions `dDBI`

, `pDBI`

, `qDBI`

and `rDBI`

define the density, distribution function, quantile function and random generation for the double binomial, `DBI()`

, distribution. The function `GetBI_C`

calculates numericaly the constant of proportionality needed for the pdf to sum up to 1.

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`mu.link` |
the link function for |

`sigma.link` |
the link function for |

`x, q` |
vector of (non-negative integer) quantiles |

`bd` |
vector of binomial denominator |

`p` |
vector of probabilities |

`mu` |
the |

`sigma` |
the |

`lower.tail` |
logical; if |

`log, log.p` |
logical; if |

`n` |
how many random values to generate |

The definition for the Double Poisson distribution first introduced by Efron (1986) is:

*f(y| n, μ,σ)=[1/C(n,μ,σ)] [Γ(n+1)/Γ(y+1)Γ(n-y+1)] [y^y (n-y)^{n-y}/n^n][n^{n/σ} μ^{y/σ} ( 1-μ)^{(n-y)/σ}/ y^{y/σ} ( n-y)^{(n-y)/σ}]*

for *y=0,1,2, ...,Inf*, *μ>0* and *σ>0* where *C* is the constant of proportinality which is calculated numerically using the function `GetBI_C()`

.

The function `DBI`

returns a `gamlss.family`

object which can be used to fit a double binomial distribution in the `gamlss()`

function.

Mikis Stasinopoulos, Bob Rigby, Marco Enea and Fernanda de Bastiani

Efron, B., 1986. Double exponential families and their use in generalized linear Regression. Journal of the American Statistical Association 81 (395), 709-721.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),
*Appl. Statist.*, **54**, part 3, pp 507-554.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
*Journal of Statistical Software*, Vol. **23**, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)
*Flexible Regression and Smoothing: Using GAMLSS in R*, Chapman and Hall/CRC.

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mstasinopoulos/GAMLSS-Distibutions documentation built on Sept. 23, 2017, 10:31 p.m.

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