YULE: Yule distribution for fitting a GAMLSS model

In Stan125/gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

Description

The function YULE 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 dYULE, pYULE, qYULE and rYULE define the density, distribution function, quantile function and random generation for the YULE parameterization of the Yule distribution.

Usage

YULE(mu.link = "log")
dYULE(x, mu = 2, log = FALSE)
pYULE(q, mu = 2, lower.tail = TRUE, log.p = FALSE) 
qYULE(p, mu = 2, lower.tail = TRUE, log.p = FALSE, 
    max.value = 10000)
rYULE(n, mu = 2)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
x	vector of (non-negative integer) quantiles.
q	vector of quantiles.
p	vector of probabilities.
n	number of random values to return.
mu	vector of positive mu values.
lower.tail	logical; if TRUE (default) probabilities are P[Y≤q y], otherwise, P[Y>y].
log, log.p	logical; if TRUE probabilities p are given as log(p).
max.value	constant; generates a sequence of values for the cdf function.

Details

The Yule distribution has density

f(y|μ)=(1/μ+1) B(y+1, 1/μ +2)

for y=0,1,2,… and mu>0.

Value

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

Author(s)

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos.

References

Wimmer, G. and Altmann, G. (1999) Thesaurus of univariate discrete probability distributions. Stamm.

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, dYULE(y), type="h")
q <- seq(0, 20, 1)
plot(q, pYULE(q), type="h")
p<-seq(0.0001,0.999,0.05)
plot(p , qYULE(p), type="s")
dat <- rYULE(100)
hist(dat)
#summary(gamlss(dat~1, family=YULE))

Stan125/gamlss.dist documentation built on May 12, 2019, 7:38 a.m.