WA1: Waring distribution for fitting a GAMLSS

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

Description

The function WA1() defines the Waring distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(), with parameters mu and sigma. The functions dWA1, pWA1, qWA1 and rWA1 define the density, distribution function, quantile function and random generation for the WA1 parameterization of the Waring distribution.

Usage

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WA1(mu.link = "log", sigma.link = "log")
dWA1(x, mu = 2, sigma = 2, log = FALSE)
pWA1(q, mu = 2, sigma = 2, lower.tail = TRUE, log.p = FALSE)
qWA1(p, mu = 2, sigma = 2, lower.tail = TRUE, log.p = FALSE, max.value = 10000)
rWA1(n, mu = 2, sigma = 2)

Arguments

mu.link

Defines the mu.link, with "log" link as the default for the mu parameter

sigma.link

Defines the sigma.link, with "log" as the default for the sigma parameter

x, q

vector of quantiles

mu

vector of location parameter values

sigma

vector of scale 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 Pareto Type 2 distribution in the function WA1 is

f(y|mu, sigma) = Beta(sigma+y, mu+1)/Beta(sigma, mu)

for y>=0, mu>0 and sigma>0.

Value

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

Author(s)

Bob Rigby r.rigby@londonmet.ac.uk, Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Fiona McElduff F.Mcelduff@londonmet.ac.uk 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

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par(mfrow=c(2,2))
y<-seq(0,20,1)
plot(y, dWA1(y), type="h")
q <- seq(0, 20, 1)
plot(q, pWA1(q), type="h")
p<-seq(0.0001,0.999,0.05)
plot(p , qWA1(p), type="s")
dat <- rWA1(100)
hist(dat)
#summary(gamlss(dat~1, family="WA1"))

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

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