gamlss.dist: WARING – R documentation

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WARING

Waring distribution for fitting a GAMLSS model

Description

The function WARING() defines the Waring distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(), with mean equal to the parameter mu and scale parameter sigma. The functions dWARING, pWARING, qWARING and rWARING define the density, distribution function, quantile function and random generation for the WARING parameterization of the Waring distribution.

Usage

WARING(mu.link = "log", sigma.link = "log")
dWARING(x, mu = 2, sigma = 2, log = FALSE)
pWARING(q, mu = 2, sigma = 2, lower.tail = TRUE, log.p = FALSE) 
qWARING(p, mu = 2, sigma = 2, lower.tail = TRUE, log.p = FALSE, 
    max.value = 10000)
rWARING(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" link as the default for the sigma 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.
`sigma`	vector of positive `sigma` 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 Waring distribution has density,

f(y|mu, sigma)= ((1+sigma) Gamma(y+mu/sigma) Gamma((mu+sigma+1)/sigma))/(sigma Gamma(y+(mu+1)/sigma+2) Gamma(mu/sigma))

for y=0,1,2,…, 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)

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos. f.mcelduff@ich.ucl.ac.uk

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.

Examples

par(mfrow=c(2,2))
y<-seq(0,20,1)
plot(y, dWARING(y), type="h")
q <- seq(0, 20, 1)
plot(q, pWARING(q), type="h")
p<-seq(0.0001,0.999,0.05)
plot(p , qWARING(p), type="s")
dat <- rWARING(100)
hist(dat)
#summary(gamlss(dat~1, family=WARING))

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