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

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.

1 2 3 4 5 6 7 8 9 10 | ```
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)
``` |

`mu.link` |
Defines the |

`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 |

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*.

returns a `gamlss.family`

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

function.

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos.

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.

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. (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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
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"))
``` |

```
Loading required package: MASS
```

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.