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

The `NBII()`

function defines the Negative Binomial type II distribution, a two parameter distribution, for a `gamlss.family`

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

.
The functions `dNBII`

, `pNBII`

, `qNBII`

and `rNBII`

define the density, distribution function, quantile function and random
generation for the Negative Binomial type II, `NBII()`

, distribution.

1 2 3 4 5 |

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

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

`mu` |
vector of positive means |

`sigma` |
vector of positive despersion parameter |

`p` |
vector of probabilities |

`q` |
vector of quantiles |

`n` |
number of random values to return |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p) |

`lower.tail` |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x] |

Definition file for Negative Binomial type II distribution.

*P(Y=y|μ,σ)=
Γ(y+μ/σ) σ^y / Γ(μ/σ)Γ(y+1) (1+σ)^{y+μ/σ}*

for *y=0,1,2, ...,Inf*, *μ>0* and *σ>0*.
This parameterization was used by Evans (1953) and also by Johnson *et al.* (1993) p 200.

returns a `gamlss.family`

object which can be used to fit a Negative Binomial type II distribution in the `gamlss()`

function.

*mu* is the mean and *((1+sigma)*mu)**0.5* is the standard deviation of the Negative Binomial type II distribution, so
*sigma* is a dispersion parameter

Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou

Evans, D. A. (1953). Experimental evidence concerning contagious distributions in ecology. *Biometrika*, **40**: 186-211.

Johnson, N. L., Kotz, S. and Kemp, A. W. (1993). *Univariate Discrete Distributions*,
2nd edn. Wiley, New York.

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in http://www.gamlss.com/.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.com/).

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.

`gamlss.family`

, `NBI`

, `PIG`

,
`SI`

1 2 3 4 5 6 7 8 9 10 11 | ```
NBII() # gives information about the default links for the Negative Binomial type II distribution
# plotting the distribution
plot(function(y) dNBII(y, mu = 10, sigma = 0.5 ), from=0, to=40, n=40+1, type="h")
# creating random variables and plot them
tN <- table(Ni <- rNBII(1000, mu=5, sigma=0.5))
r <- barplot(tN, col='lightblue')
# library(gamlss)
# data(aids)
# h<-gamlss(y~cs(x,df=7)+qrt, family=NBII, data=aids) # fits a model
# plot(h)
# pdf.plot(family=NBII, mu=10, sigma=0.5, min=0, max=40, step=1)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.