R: Poisson distribution for fitting a GAMLSS model

PO {gamlss.dist} | R Documentation

## Poisson distribution for fitting a GAMLSS model

### Description

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.

### Usage

    PO(mu.link = "log")
    dPO(x, mu = 1, log = FALSE)
    pPO(q, mu = 1, lower.tail = TRUE, log.p = FALSE)
    qPO(p, mu = 1, lower.tail = TRUE, log.p = FALSE)
    rPO(n, mu = 1)

### Arguments

`mu.link` | Defines the `mu.link`, with "log" link as the default for the mu parameter
`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]

### Details

Definition file for Poisson distribution.

f(y|μ)=e^(-μ)*μ^y/Γ(y+1)

for y=0,1,2,... and μ>0.

### Value

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

### Note

mu is the mean of the Poisson distribution

### Author(s)

Bob Rigby, Mikis Stasinopoulos, and Kalliope Akantziliotou

### References

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 https://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 https://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, https://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.

### See Also

`gamlss.family`, `NBI`, `NBII`, `SI`, `SICHEL`

### Examples

    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)

[Package gamlss.dist version 5.3-2 Index]