WEI2 {gamlss.dist} | R Documentation |
A specific parameterization of the Weibull distribution for fitting a GAMLSS
Description
The function WEI2
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()
.
This is the parameterization of the Weibull distribution usually used in proportional hazard models and is defined in details below.
[Note that the GAMLSS function WEI
uses a
different parameterization for fitting the Weibull distribution.]
The functions dWEI2
, pWEI2
, qWEI2
and rWEI2
define the density, distribution function, quantile function and random
generation for the specific parameterization of the Weibull distribution.
Usage
WEI2(mu.link = "log", sigma.link = "log")
dWEI2(x, mu = 1, sigma = 1, log = FALSE)
pWEI2(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qWEI2(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rWEI2(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 values |
sigma |
vector of sigma 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 |
Details
The parameterization of the function WEI2
is given by
f(y|\mu,\sigma)= \sigma\mu y^{\sigma-1}e^{-\mu
y^{\sigma}}
for y>0
, \mu>0
and \sigma>0
, see pp. 436-437 of Rigby et al. (2019).
The GAMLSS functions dWEI2
, pWEI2
, qWEI2
, and rWEI2
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 WEI
for a different parameterization of the Weibull.]
Value
WEI2()
returns a gamlss.family
object which can be used to fit a Weibull distribution in the gamlss()
function.
dWEI2()
gives the density, pWEI2()
gives the distribution
function, qWEI2()
gives the quantile function, and rWEI2()
generates random deviates. The latest functions are based on the equivalent R
functions for Weibull distribution.
Warning
In WEI2
the estimated parameters mu
and sigma
can be highly correlated so it is advisable to use the
CG()
method for fitting [as the RS() method can be veru slow in this situation.]
Note
The mean in WEI2
is given by \mu^{-1/\sigma} \Gamma (
\frac{1}{\sigma}+1 )
and the variance
\mu^{-2/\sigma} ( \Gamma ( \frac{2}{\sigma}+1 )- \left[ \Gamma (
\frac{1}{\sigma}+1 )\right]^2
)
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
WEI2()
dat<-rWEI(100, mu=.1, sigma=2)
hist(dat)
# library(gamlss)
# gamlss(dat~1, family=WEI2, method=CG())