R: Geometric distribution for fitting a GAMLSS model

GEOM {gamlss.dist} | R Documentation

## Geometric distribution for fitting a GAMLSS model

### Description

The functions `GEOMo()` and `GEOM()` define two parametrizations of the geometric distribution. The geometric distribution is a one parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The mean of `GEOM()` is equal to the parameter `mu`. The functions `dGEOM`, `pGEOM`, `qGEOM` and `rGEOM` define the density, distribution function, quantile function and random generation for the `GEOM` parameterization of the Geometric distribution.

### Usage

    GEOM(mu.link = "log")
    dGEOM(x, mu = 2, log = FALSE)
    pGEOM(q, mu = 2, lower.tail = TRUE, log.p = FALSE)
    qGEOM(p, mu = 2, lower.tail = TRUE, log.p = FALSE)
    rGEOM(n, mu = 2)
    GEOMo(mu.link = "logit")
    dGEOMo(x, mu = 0.5, log = FALSE)
    pGEOMo(q, mu = 0.5, lower.tail = TRUE, log.p = FALSE)
    qGEOMo(p, mu = 0.5, lower.tail = TRUE, log.p = FALSE)
    rGEOMo(n, mu = 0.5)

### Arguments

`mu.link` | Defines the `mu.link`, with `log` link as the default for the `mu` parameter
`x, q` | vector of quantiles
`mu` | vector of location parameter values
`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]
`p` | vector of probabilities
`n` | number of observations. If `length(n) > 1`, the length is taken to be the number required

### Details

The parameterization of the original geometric distribution in the function `GE` is

f(y|μ) = (1-μ)^y μ

for y>=0 and μ>0.

The parameterization of the geometric distribution in the function `GEOM` is

f(y|μ) = μ^y/(μ+1)^{y+1}

where for y>=0 and μ>0.

### Value

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

### Author(s)

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos.

### References

Johnson, N. L., Kemp, A. W., and Kotz, S. (2005). Univariate discrete distributions. Wiley.

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.

### See Also

`gamlss.family`

### Examples

    par(mfrow=c(2,2))
    y<-seq(0,20,1)
    plot(y, dGEOM(y), type="h")
    q <- seq(0, 20, 1)
    plot(q, pGEOM(q), type="h")
    p<-seq(0.0001,0.999,0.05)
    plot(p , qGEOM(p), type="s")
    dat <- rGEOM(100)
    hist(dat)
    #summary(gamlss(dat~1, family=GEOM))
    par(mfrow=c(2,2))
    y<-seq(0,20,1)
    plot(y, dGEOMo(y), type="h")
    q <- seq(0, 20, 1)
    plot(q, pGEOMo(q), type="h")
    p<-seq(0.0001,0.999,0.05)
    plot(p , qGEOMo(p), type="s")
    dat <- rGEOMo(100)
    hist(dat)
    #summary(gamlss(dat~1, family="GE"))

[Package gamlss.dist version 5.0-2 Index]