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

This function `PO`

defines the Poisson distribution, an one parameter distribution, for a `gamlss.family`

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

. The functions `dPO`

, `pPO`

, `qPO`

and `rPO`

define the density, distribution function, quantile function and random
generation for the Poisson, `PO()`

, distribution.

1 2 3 4 5 |

`mu.link` |
Defines the |

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

`mu` |
vector of positive means |

`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 Poisson distribution.

*f(y|μ)=e^(-μ)*μ^y/Γ(y+1)*

for *y=0,1,2,...* and *μ>0*.

returns a `gamlss.family`

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

function.

*mu* is the mean of the Poisson distribution

Bob Rigby, Mikis Stasinopoulos [email protected], and Kalliope Akantziliotou

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. 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.org/).

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`

, `NBII`

,
`SI`

, `SICHEL`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
PO()# gives information about the default links for the Poisson distribution
# fitting data using PO()
# plotting the distribution
plot(function(y) dPO(y, mu=10 ), from=0, to=20, n=20+1, type="h")
# creating random variables and plot them
tN <- table(Ni <- rPO(1000, mu=5))
r <- barplot(tN, col='lightblue')
# library(gamlss)
# data(aids)
# h<-gamlss(y~cs(x,df=7)+qrt, family=PO, data=aids) # fits the constant+x+qrt model
# plot(h)
# pdf.plot(family=PO, mu=10, min=0, max=20, step=1)
``` |

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

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