Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples
The function LOGNO
defines a gamlss.family
distribution to fits the log-Normal distribution.
The function LNO
is more general and can fit a Box-Cox transformation
to data using the gamlss()
function.
In the LOGNO
there are two parameters involved mu
sigma
, while in the
LNO
there are three parameters mu
sigma
,
and the transformation parameter nu
.
The transformation parameter nu
in LNO
is a 'fixed' parameter (not estimated) and it has its default value equal to
zero allowing the fitting of the log-normal distribution as in LOGNO
.
See the example below on how to fix nu
to be a particular value.
In order to estimate (or model) the parameter nu
, use the gamlss.family
BCCG
distribution which uses a reparameterized version of the the Box-Cox transformation.
The functions dLOGNO
, pLOGNO
, qLOGNO
and rLOGNO
define the density, distribution function, quantile function and random
generation for the specific parameterization of the log-normal distribution.
The functions dLNO
, pLNO
, qLNO
and rLNO
define the density, distribution function, quantile function and random
generation for the specific parameterization of the log-normal distribution and more generally a Box-Cox transformation.
1 2 3 4 5 6 7 8 9 10 | LNO(mu.link = "identity", sigma.link = "log")
LOGNO(mu.link = "identity", sigma.link = "log")
dLNO(x, mu = 1, sigma = 0.1, nu = 0, log = FALSE)
dLOGNO(x, mu = 0, sigma = 1, log = FALSE)
pLNO(q, mu = 1, sigma = 0.1, nu = 0, lower.tail = TRUE, log.p = FALSE)
pLOGNO(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qLNO(p, mu = 1, sigma = 0.1, nu = 0, lower.tail = TRUE, log.p = FALSE)
qLOGNO(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rLNO(n, mu = 1, sigma = 0.1, nu = 0)
rLOGNO(n, mu = 0, sigma = 1)
|
mu.link |
Defines the |
sigma.link |
Defines the |
x,q |
vector of quantiles |
mu |
vector of location parameter values |
sigma |
vector of scale parameter values |
nu |
vector of shape 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 |
The probability density function in LOGNO
is defined as
f(y|mu,sigma)=(1/(y*sqrt(2*pi)*sigma))*exp(-0.5*((log(y)-mu)/(sigma))^2)
for y>0, mu=(-Inf,+Inf) and σ>0.
The probability density function in LNO
is defined as
f(y|mu,sigma,nu)=(1/(sqrt(2*pi)*sigma))*(y^(nu-1))*exp(-((z-mu)/(2sigma))^2)
where if ν!=0 z=(y^nu-1)/nu else z=\log(y) and z \sim N(0,σ^2), for y>0, μ>0, σ>0 and ν=(-Inf,+Inf).
LNO()
returns a gamlss.family
object which can be used to fit a log-narmal distribution in the gamlss()
function.
dLNO()
gives the density, pLNO()
gives the distribution
function, qLNO()
gives the quantile function, and rLNO()
generates random deviates.
This is a two parameter fit for mu and sigma while nu is fixed.
If you wish to model nu use the gamlss family BCCG
.
mu is the mean of z (and also the median of y), the Box-Cox transformed variable and sigma is the standard deviation of z and approximate the coefficient of variation of y
Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou
Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations (with discussion), J. R. Statist. Soc. B., 26, 211–252
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.
1 2 3 4 5 6 7 8 | LOGNO()# gives information about the default links for the log normal distribution
LNO()# gives information about the default links for the Box Cox distribution
# library(gamlss)
# data(abdom)
# h1<-gamlss(y~cs(x), family=LOGNO, data=abdom)#fits the log-Normal distribution
# h2<-gamlss(y~cs(x), family=LNO, data=abdom) #should be identical to the one above
# to change to square root transformation, i.e. fix nu=0.5
# h3<-gamlss(y~cs(x), family=LNO, data=abdom, nu.fix=TRUE, nu.start=0.5)
|
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