YU2: Yule distribution for fitting a GAMLSS

In gamlss.dist: Distributions to be used for GAMLSS modelling.

Description

The function YU2() defines the Yule distribution, a one parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(), with mean equal to the parameter mu. The functions dYU2, pYU2, qYU2 and rYU2 define the density, distribution function, quantile function and random generation for the YU2 parameterization of the Yule distribution.

Usage

YU2(mu.link = "log")
dYU2(x, mu = 2, log = FALSE)
pYU2(q, mu = 2, lower.tail = TRUE, log.p = FALSE)
qYU2(p, mu = 2, lower.tail = TRUE, log.p = FALSE, max.value=10000)
rYU2(n, mu = 2)

Arguments

mu.link	Defines the mu.link, with "log" link sa 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
max.value	constant; generates a sequence of values for the cdf function

Details

The parameterization of the Yule distribution in the function YU2 is

f(y|lambda) = Beta(lambda+1, y+1)/Beta(lambda, 1)

where lamda = 1/mu + 1 for y>=0 and mu>0.

Value

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

Note

For the function YU1(), mu is the mean of the Yule distribution.

Author(s)

Bob Rigby [e-mail], Mikis Stasinopoulos [e-mail], Fiona McElduff [e-mail] 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.

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.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.

See Also

gamlss.family

Examples

par(mfrow=c(2,2))
y<-seq(0,20,1)
plot(y, dYU2(y), type="h")
q <- seq(0, 20, 1)
plot(q, pYU2(q), type="h")
p<-seq(0.0001,0.999,0.05)
plot(p , qYU2(p), type="s")
dat <- rYU2(100)
hist(dat)
#summary(gamlss(dat~1, family=YU2))

gamlss.dist documentation built on May 2, 2019, 5:20 p.m.