WEI {gamlss.dist} | R Documentation |
Weibull distribution for fitting a GAMLSS
Description
The function WEI
can be used to define the Weibull distribution, a two parameter distribution, for a
gamlss.family
object to be used in GAMLSS fitting using the function gamlss()
. [Note that the GAMLSS function WEI2
uses a
different parameterization for fitting the Weibull distribution.]
The functions dWEI
, pWEI
, qWEI
and rWEI
define the density, distribution function, quantile function and random
generation for the specific parameterization of the Weibul distribution.
Usage
WEI(mu.link = "log", sigma.link = "log")
dWEI(x, mu = 1, sigma = 1, log = FALSE)
pWEI(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qWEI(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rWEI(n, mu = 1, sigma = 1)
Arguments
mu.link |
Defines the |
sigma.link |
Defines the |
x , q |
vector of quantiles |
mu |
vector of the mu parameter |
sigma |
vector of sigma parameter |
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 |
Details
The parameterization of the function WEI
is given by
for ,
and
see pp. 435-436 of Rigby et al. (2019).
The GAMLSS functions
dWEI
, pWEI
, qWEI
, and rWEI
can be used to provide the pdf, the cdf, the quantiles and
random generated numbers for the Weibull distribution with argument mu
, and sigma
.
[See the GAMLSS function WEI2
for a different parameterization of the Weibull.]
Value
WEI()
returns a gamlss.family
object which can be used to fit a Weibull distribution in the gamlss()
function.
dWEI()
gives the density, pWEI()
gives the distribution
function, qWEI()
gives the quantile function, and rWEI()
generates random deviates. The latest functions are based on the equivalent R
functions for Weibull distribution.
Note
The mean in WEI
is given by and the variance
Author(s)
Mikis Stasinopoulos, Bob Rigby and Calliope 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.
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
(see also https://www.gamlss.com/).
See Also
Examples
WEI()
dat<-rWEI(100, mu=10, sigma=2)
# library(gamlss)
# gamlss(dat~1, family=WEI)