DEL {gamlss.dist} | R Documentation |
The Delaporte distribution for fitting a GAMLSS model
Description
The DEL()
function defines the Delaporte distribution, a three parameter discrete distribution, for a gamlss.family
object to be used
in GAMLSS fitting using the function gamlss()
.
The functions dDEL
, pDEL
, qDEL
and rDEL
define the density, distribution function, quantile function and random
generation for the Delaporte DEL()
, distribution.
Usage
DEL(mu.link = "log", sigma.link = "log", nu.link = "logit")
dDEL(x, mu=1, sigma=1, nu=0.5, log=FALSE)
pDEL(q, mu=1, sigma=1, nu=0.5, lower.tail = TRUE,
log.p = FALSE)
qDEL(p, mu=1, sigma=1, nu=0.5, lower.tail = TRUE,
log.p = FALSE, max.value = 10000)
rDEL(n, mu=1, sigma=1, nu=0.5, max.value = 10000)
Arguments
mu.link |
Defines the |
sigma.link |
Defines the |
nu.link |
Defines the |
x |
vector of (non-negative integer) quantiles |
mu |
vector of positive mu |
sigma |
vector of positive dispersion parameter |
nu |
vector of nu |
p |
vector of probabilities |
q |
vector of quantiles |
n |
number of random values to return |
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] |
max.value |
a constant, set to the default value of 10000 for how far the algorithm should look for q |
Details
The probability function of the Delaporte distribution is given by
where
for
where
,
and
.
This distribution is a parametrization of the distribution given by Wimmer and Altmann (1999) p 515-516 where
,
and
.
For more details see pp 506-507 of Rigby et al. (2019).
Value
Returns a gamlss.family
object which can be used to fit a Delaporte distribution in the gamlss()
function.
Note
The mean of is given by
and the variance by
.
Author(s)
Rigby, R. A., Stasinopoulos D. M. and Marco Enea
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.
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,doi:10.1201/9780429298547. 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, doi:10.18637/jss.v023.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. doi:10.1201/b21973
Wimmer, G. and Altmann, G (1999). Thesaurus of univariate discrete probability distributions . Stamn Verlag, Essen, Germany
(see also https://www.gamlss.com/).
See Also
Examples
DEL()# gives information about the default links for the Delaporte distribution
#plot the pdf using plot
plot(function(y) dDEL(y, mu=10, sigma=1, nu=.5), from=0, to=100, n=100+1, type="h") # pdf
# plot the cdf
plot(seq(from=0,to=100),pDEL(seq(from=0,to=100), mu=10, sigma=1, nu=0.5), type="h") # cdf
# generate random sample
tN <- table(Ni <- rDEL(100, mu=10, sigma=1, nu=0.5))
r <- barplot(tN, col='lightblue')
# fit a model to the data
# libary(gamlss)
# gamlss(Ni~1,family=DEL, control=gamlss.control(n.cyc=50))