gamlss.dist: GEOM – R documentation

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GEOM

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.

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. (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.

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"))

gamlss.dist

Distributions for Generalized Additive Models for Location Scale and Shape

v5.3-2

GPL-2 | GPL-3

Authors

Mikis Stasinopoulos [aut, cre, cph], Robert Rigby [aut], Calliope Akantziliotou [ctb], Vlasios Voudouris [ctb], Gillian Heller [ctb], Fernanda De Bastiani [ctb], Raydonal Ospina [ctb], Nicoletta Motpan [ctb], Fiona McElduff [ctb], Majid Djennad [ctb], Marco Enea [ctb], Alexios Ghalanos [ctb], Christos Argyropoulos [ctb], Almond Stocker [ctb], Jens Lichter [ctb], Stanislaus Stadlmann [ctb]

Initial release

2021-03-08