R/BCT.R
In mstasinopoulos/GAMLSS-Distibutions: Distributions for Generalized Additive Models for Location Scale and Shape
Defines functions
rBCTo
qBCTo
pBCTo
dBCTo
Documented in
dBCTo
pBCTo
qBCTo
rBCTo
# last change : MS Wednesday, September 17, 2003 at 08:45
BCT <- function (mu.link="identity", sigma.link="log", nu.link ="identity", tau.link="log")
{
mstats <- checklink("mu.link", "Box Cox t ", substitute(mu.link),
c("inverse", "log", "identity", "own"))
dstats <- checklink("sigma.link", "Box Cox t ", substitute(sigma.link),
c("inverse", "log", "identity", "own"))
vstats <- checklink("nu.link", "Box Cox t ",substitute(nu.link),
c("inverse", "log", "identity", "own"))
tstats <- checklink("tau.link", "Box Cox t ",substitute(tau.link),
c("inverse", "log", "identity", "own"))
structure(
list(family = c("BCT", "Box-Cox t"),
parameters = list(mu=TRUE, sigma=TRUE, nu=TRUE, tau=TRUE),
nopar = 4,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
tau.link = as.character(substitute(tau.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
tau.linkfun = tstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
tau.linkinv = tstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
tau.dr = tstats$mu.eta,
dldm = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
dldm <- (w*z)/(mu*sigma)+(nu/mu)*(w*(z^2)-1)
dldm
},
d2ldm2 = function(mu,sigma,nu,tau){
d2ldm2 <- -(tau+2*nu*nu*sigma*sigma*tau+1)/(tau+3)
d2ldm2 <- d2ldm2/(mu*mu*sigma*sigma)
},
dldd = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldd <- (w*(z^2)-1)/sigma + h/(sigma^2*abs(nu))
dldd
} ,
d2ldd2 = function(sigma, tau) -2*tau/(sigma^2*(tau+3)),
dldv = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldv <- ((w*z^2)/nu)-log(y/mu) *(w*z^2+((w*z)/(sigma*nu))-1)
dldv <- dldv+sign(nu)*h/(sigma*nu^2)
} ,
d2ldv2 = function(sigma) {
-7*(sigma^2)/4
},
dldt = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
j <- (log(pt(1/(sigma*abs(nu)),df=tau+0.01))
-log(pt(1/(sigma*abs(nu)),df=tau)))/0.01
dldt <- -0.5*log(1+(z^2)/tau)+(w*(z^2))/(2*tau)
dldt <- dldt+0.5*digamma((tau+1)/2)-0.5*digamma(tau/2)-1/(2*tau)-j
} ,
d2ldt2 = function(tau) {
d2ldt2 <- trigamma((tau+1)/2) -trigamma(tau/2) +2*(tau+5)/(tau*(tau+1)*(tau+3))
d2ldt2 <- d2ldt2/4
d2ldt2 <- ifelse(d2ldt2 < -1e-15, d2ldt2,-1e-15)
d2ldt2
} ,
d2ldmdd = function(mu,sigma,nu,tau) -(2*nu*tau)/(mu*sigma*(tau+3)),
d2ldmdv = function(mu,tau) (tau-3)/(2*mu*(tau+3)),
d2ldmdt = function(mu,nu,tau) (2*nu)/(mu*(tau+1)*(tau+3)),
d2ldddv = function(sigma,nu,tau) -(sigma*nu*tau)/(tau+3),
d2ldddt = function(sigma,tau) 2/(sigma*(tau+1)*(tau+3)),
d2ldvdt = function(sigma,nu,tau) (2*sigma^2*nu)/(tau^2),
G.dev.incr = function(y,mu,sigma,nu,tau,...)
-2*dBCT(y,mu,sigma,nu,tau,log=TRUE),
rqres = expression(rqres(pfun="pBCT", type="Continuous", y=y, mu=mu, sigma=sigma, nu=nu, tau=tau)) ,
mu.initial = expression(mu <- (y+mean(y))/2),
sigma.initial = expression(sigma<- rep(0.1, length(y))),
nu.initial = expression(nu <- rep(0.5, length(y))),
tau.initial = expression(tau <-rep(10, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) TRUE ,
tau.valid = function(tau) all(tau > 0),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family","family"))
}
#-----------------------------------------------------------------
dBCT <- dBCTo <- function(x, mu=5, sigma=0.1, nu=1, tau=2, log=FALSE)
{
if (any(mu <= 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau <= 0)) stop(paste("tau must be positive", "\n", ""))
# if (any(x < 0)) stop(paste("x must be positive", "\n", ""))
if(length(nu)>1) z <- ifelse(nu != 0,(((x/mu)^nu-1)/(nu*sigma)),log(x/mu)/sigma)
else if (nu != 0) z <- (((x/mu)^nu-1)/(nu*sigma)) else z <- log(x/mu)/sigma
loglik <- (nu-1)*log(x)-nu*log(mu)-log(sigma)
fTz <- lgamma((tau+1)/2)-lgamma(tau/2)-0.5*log(tau)-lgamma(0.5)
fTz <- fTz-((tau+1)/2)* log(1+(z*z)/tau)
loglik <- loglik+fTz-log(pt(1/(sigma*abs(nu)),df=tau))
if (length(tau)>1) loglik <- ifelse(tau>1000000, dBCCG(x,mu,sigma,nu,log=TRUE), loglik) # MS Wednesday, April 12, 2006
else if (tau>1000000) loglik <- dBCCG(x,mu,sigma,nu,log=TRUE)
ft <- if(log==FALSE) exp(loglik) else loglik
ft <-ifelse(x <= 0, 0, ft)
ft
}
#-----------------------------------------------------------------
pBCT <- pBCTo <- function(q, mu=5, sigma=0.1, nu=1, tau=2, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu < 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau < 0)) stop(paste("tau must be positive", "\n", ""))
# if (any(q < 0)) stop(paste("y must be positive", "\n", ""))
if(length(nu)>1) z <- ifelse(nu != 0,(((q/mu)^nu-1)/(nu*sigma)),log(q/mu)/sigma)
else if (nu != 0) z <- (((q/mu)^nu-1)/(nu*sigma)) else z <- log(q/mu)/sigma
FYy1 <- pt(z,tau)
if(length(nu)>1) FYy2 <- ifelse(nu > 0, pt(-1/(sigma*abs(nu)),df=tau) ,0)
else if (nu>0) FYy2 <- pt(-1/(sigma*abs(nu)),df=tau) else FYy2 <- 0
FYy3 <- pt(1/(sigma*abs(nu)),df=tau)
FYy <- (FYy1-FYy2)/FYy3
if(lower.tail==TRUE) FYy <- FYy else FYy <- 1-FYy
if(log.p==FALSE) FYy <- FYy else FYy<- log(FYy)
FYy <-ifelse(q <= 0, 0, FYy)
FYy
}
#-----------------------------------------------------------------
qBCT <- qBCTo <- function(p, mu=5, sigma=0.1, nu=1, tau=2, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu < 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau < 0)) stop(paste("tau must be positive", "\n", ""))
if (log.p==TRUE) p <- exp(p) else p <- p
if (any(p <= 0)|any(p >= 1)) stop(paste("p must be between 0 and 1", "\n", ""))
if (lower.tail==TRUE) p <- p else p <- 1-p
if(length(nu)>1)
{
z <- ifelse((nu<=0),qt(p*pt(1/(sigma*abs(nu)),tau),tau),qt(1-(1-p)*pt(1/(sigma*abs(nu)),tau),tau))
}
else {
z <- if (nu<=0) qt(p*pt(1/(sigma*abs(nu)),tau),tau)
else qt(1-(1-p)*pt(1/(sigma*abs(nu)),tau),tau)
}
if(length(nu)>1) ya <- ifelse(nu != 0,mu*(nu*sigma*z+1)^(1/nu),mu*exp(sigma*z))
else if (nu != 0) ya <- mu*(nu*sigma*z+1)^(1/nu) else ya <- mu*exp(sigma*z)
ya
}
#-----------------------------------------------------------------
rBCT <- rBCTo <- function(n, mu=5, sigma=0.1, nu=1, tau=2)
{
if (any(mu <= 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau <= 0)) stop(paste("tau must be positive", "\n", ""))
if (any(n <= 0)) stop(paste("n must be a positive integer", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qBCT(p,mu=mu,sigma=sigma,nu=nu,tau=tau)
r
}
#-----------------------------------------------------------------
BCTuntr <- function (mu.link="identity", sigma.link="log", nu.link ="identity", tau.link="log")
{
mstats <- checklink("mu.link", "Box Cox t ", substitute(mu.link), c("1/mu^2", "log", "identity"))
dstats <- checklink("sigma.link", "Box Cox t ", substitute(sigma.link), c("inverse", "log", "identity"))
vstats <- checklink("nu.link", "Box Cox t ",substitute(nu.link), c("1/nu^2", "log", "identity"))
tstats <- checklink("tau.link", "Box Cox t ",substitute(tau.link), c("1/tau^2", "log", "identity"))
structure(
list(family = c("BCTuntr", "Box-Cox t untrucated"),
parameters = list(mu=TRUE, sigma=TRUE, nu=TRUE, tau=TRUE),
nopar = 4,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
tau.link = as.character(substitute(tau.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
tau.linkfun = tstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
tau.linkinv = tstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
tau.dr = tstats$mu.eta,
dldm = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
dldm <- k*u*(z/mu)+(nu/mu)*(u*(z*z)-1)
dldm
},
d2ldm2 = function(mu,sigma,nu,tau){
d2ldm2 <- -(tau+2*nu*nu*sigma*sigma*tau+1)/(tau+3)
d2ldm2 <- d2ldm2/(mu*mu*sigma*sigma)
},
dldd = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
dldd <- k*(u*(z*z)-1)
dldd
} ,
d2ldd2 = function(sigma,tau) -2*tau/(sigma^2*(tau+3)),
dldv = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
lnybym <- log(y/mu)
dldv <- ((u*z)/nu)*(z-(lnybym*k))
dldv <- dldv-lnybym*(u*z*z-1)
} ,
d2ldv2 = function(sigma) {
-7*(sigma^2)/4
},
dldt = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
#t2 <- tau/2
#t3 <- (tau+1)/2
dldt <- -0.5*log(1+(z*z)/tau)+0.5*u*(z*z)/tau
dldt <- dldt+0.5*digamma((tau+1)/2)-0.5*digamma(tau/2)-1/(2*tau)
} ,
d2ldt2 = function(tau) {
t2 <- tau/2
t3 <- (tau+1)/2
d2ldt2 <- trigamma(t3) -trigamma(t2) +2*(tau+5)/(tau*(tau+1)*(tau+3))
d2ldt2 <- d2ldt2/4
d2ldt2 <- ifelse(d2ldt2 < -1e-15, d2ldt2,-1e-15)
d2ldt2
} ,
d2ldmdd = function(mu,sigma,nu,tau) -(2*nu*tau)/(mu*sigma*(tau+3)),
d2ldmdv = function(mu,tau) (tau-3)/(2*mu*(tau+3)),
d2ldmdt = function(mu,nu,tau) (2*nu)/(mu*(tau+1)*(tau+3)),
d2ldddv = function(sigma,nu,tau) -(sigma*nu*tau)/(tau+3),
d2ldddt = function(sigma,tau) 2/(sigma*(tau+1)*(tau+3)),
d2ldvdt = function(sigma,nu,tau) (2*sigma^2*nu)/(tau^2),
G.dev.incr = function(y,mu,sigma,nu,tau,...) {
tf <- pt(1/(sigma*abs(nu)),tau)
if(any(tf<.99))
warning(paste("The truncation factor F(1/(sigma*|nu|)) \n",
"of BCT is less than 0.99 for some observations",
"\n"))
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z + ifelse(nu == 0,1,0)*log(y/mu)*k
lik <- (nu*log(y/mu)-log(y)+log(k))
lik <- lik+lgamma((tau+1)/2)-lgamma(tau/2)-0.5*log(tau)-lgamma(0.5)
lik <- lik-((tau+1)/2)* log(1+(z*z)/tau)
G.dev.incr <- -2*lik
G.dev.incr
} ,
rqres =expression( {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z + ifelse(nu == 0,1,0)*log(y/mu)*k
rqres <- qnorm(pt(z,tau))
}) ,
mu.initial = expression(mu <- y),
sigma.initial = expression(sigma<- rep(0.1, length(y))),
nu.initial = expression(nu <- rep(0.5, length(y))),
tau.initial = expression(tau <-rep(10, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) TRUE ,
tau.valid = function(tau) all(tau > 0),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family","family"))
}
#-----------------------------------------------------------------------------------------
BCTo <- function (mu.link="log", sigma.link="log", nu.link ="identity", tau.link="log")
{
mstats <- checklink("mu.link", "Box Cox t ", substitute(mu.link),
c("inverse", "log", "identity", "own"))
dstats <- checklink("sigma.link", "Box Cox t ", substitute(sigma.link),
c("inverse", "log", "identity", "own"))
vstats <- checklink("nu.link", "Box Cox t ",substitute(nu.link),
c("inverse", "log", "identity", "own"))
tstats <- checklink("tau.link", "Box Cox t ",substitute(tau.link),
c("inverse", "log", "identity", "own"))
structure(
list(family = c("BCTo", "Box-Cox-t-orig."),
parameters = list(mu=TRUE, sigma=TRUE, nu=TRUE, tau=TRUE),
nopar = 4,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
tau.link = as.character(substitute(tau.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
tau.linkfun = tstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
tau.linkinv = tstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
tau.dr = tstats$mu.eta,
dldm = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
dldm <- (w*z)/(mu*sigma)+(nu/mu)*(w*(z^2)-1)
dldm
},
d2ldm2 = function(mu,sigma,nu,tau){
d2ldm2 <- -(tau+2*nu*nu*sigma*sigma*tau+1)/(tau+3)
d2ldm2 <- d2ldm2/(mu*mu*sigma*sigma)
},
dldd = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldd <- (w*(z^2)-1)/sigma + h/(sigma^2*abs(nu))
dldd
} ,
d2ldd2 = function(sigma, tau) -2*tau/(sigma^2*(tau+3)),
dldv = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldv <- ((w*z^2)/nu)-log(y/mu) *(w*z^2+((w*z)/(sigma*nu))-1)
dldv <- dldv+sign(nu)*h/(sigma*nu^2)
} ,
d2ldv2 = function(sigma) {
-7*(sigma^2)/4
},
dldt = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
j <- (log(pt(1/(sigma*abs(nu)),df=tau+0.01))
-log(pt(1/(sigma*abs(nu)),df=tau)))/0.01
dldt <- -0.5*log(1+(z^2)/tau)+(w*(z^2))/(2*tau)
dldt <- dldt+0.5*digamma((tau+1)/2)-0.5*digamma(tau/2)-1/(2*tau)-j
} ,
d2ldt2 = function(tau) {
d2ldt2 <- trigamma((tau+1)/2) -trigamma(tau/2) +2*(tau+5)/(tau*(tau+1)*(tau+3))
d2ldt2 <- d2ldt2/4
d2ldt2 <- ifelse(d2ldt2 < -1e-15, d2ldt2,-1e-15)
d2ldt2
} ,
d2ldmdd = function(mu,sigma,nu,tau) -(2*nu*tau)/(mu*sigma*(tau+3)),
d2ldmdv = function(mu,tau) (tau-3)/(2*mu*(tau+3)),
d2ldmdt = function(mu,nu,tau) (2*nu)/(mu*(tau+1)*(tau+3)),
d2ldddv = function(sigma,nu,tau) -(sigma*nu*tau)/(tau+3),
d2ldddt = function(sigma,tau) 2/(sigma*(tau+1)*(tau+3)),
d2ldvdt = function(sigma,nu,tau) (2*sigma^2*nu)/(tau^2),
G.dev.incr = function(y,mu,sigma,nu,tau,...)
-2*dBCTo(y,mu,sigma,nu,tau,log=TRUE),
rqres = expression(rqres(pfun="pBCTo", type="Continuous", y=y, mu=mu, sigma=sigma, nu=nu, tau=tau)) ,
mu.initial = expression(mu <- (y+mean(y))/2),
sigma.initial = expression(sigma<- rep(0.1, length(y))),
nu.initial = expression(nu <- rep(0.5, length(y))),
tau.initial = expression(tau <-rep(10, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) TRUE ,
tau.valid = function(tau) all(tau > 0),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family","family"))
}
#------------------------------------------------------------------------
mstasinopoulos/GAMLSS-Distibutions documentation built on Nov. 3, 2023, 10:33 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Defines functions rBCTo qBCTo pBCTo dBCTo
Documented in dBCTo pBCTo qBCTo rBCTo
# last change : MS Wednesday, September 17, 2003 at 08:45
BCT <- function (mu.link="identity", sigma.link="log", nu.link ="identity", tau.link="log")
{
mstats <- checklink("mu.link", "Box Cox t ", substitute(mu.link),
c("inverse", "log", "identity", "own"))
dstats <- checklink("sigma.link", "Box Cox t ", substitute(sigma.link),
c("inverse", "log", "identity", "own"))
vstats <- checklink("nu.link", "Box Cox t ",substitute(nu.link),
c("inverse", "log", "identity", "own"))
tstats <- checklink("tau.link", "Box Cox t ",substitute(tau.link),
c("inverse", "log", "identity", "own"))
structure(
list(family = c("BCT", "Box-Cox t"),
parameters = list(mu=TRUE, sigma=TRUE, nu=TRUE, tau=TRUE),
nopar = 4,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
tau.link = as.character(substitute(tau.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
tau.linkfun = tstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
tau.linkinv = tstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
tau.dr = tstats$mu.eta,
dldm = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
dldm <- (w*z)/(mu*sigma)+(nu/mu)*(w*(z^2)-1)
dldm
},
d2ldm2 = function(mu,sigma,nu,tau){
d2ldm2 <- -(tau+2*nu*nu*sigma*sigma*tau+1)/(tau+3)
d2ldm2 <- d2ldm2/(mu*mu*sigma*sigma)
},
dldd = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldd <- (w*(z^2)-1)/sigma + h/(sigma^2*abs(nu))
dldd
} ,
d2ldd2 = function(sigma, tau) -2*tau/(sigma^2*(tau+3)),
dldv = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldv <- ((w*z^2)/nu)-log(y/mu) *(w*z^2+((w*z)/(sigma*nu))-1)
dldv <- dldv+sign(nu)*h/(sigma*nu^2)
} ,
d2ldv2 = function(sigma) {
-7*(sigma^2)/4
},
dldt = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
j <- (log(pt(1/(sigma*abs(nu)),df=tau+0.01))
-log(pt(1/(sigma*abs(nu)),df=tau)))/0.01
dldt <- -0.5*log(1+(z^2)/tau)+(w*(z^2))/(2*tau)
dldt <- dldt+0.5*digamma((tau+1)/2)-0.5*digamma(tau/2)-1/(2*tau)-j
} ,
d2ldt2 = function(tau) {
d2ldt2 <- trigamma((tau+1)/2) -trigamma(tau/2) +2*(tau+5)/(tau*(tau+1)*(tau+3))
d2ldt2 <- d2ldt2/4
d2ldt2 <- ifelse(d2ldt2 < -1e-15, d2ldt2,-1e-15)
d2ldt2
} ,
d2ldmdd = function(mu,sigma,nu,tau) -(2*nu*tau)/(mu*sigma*(tau+3)),
d2ldmdv = function(mu,tau) (tau-3)/(2*mu*(tau+3)),
d2ldmdt = function(mu,nu,tau) (2*nu)/(mu*(tau+1)*(tau+3)),
d2ldddv = function(sigma,nu,tau) -(sigma*nu*tau)/(tau+3),
d2ldddt = function(sigma,tau) 2/(sigma*(tau+1)*(tau+3)),
d2ldvdt = function(sigma,nu,tau) (2*sigma^2*nu)/(tau^2),
G.dev.incr = function(y,mu,sigma,nu,tau,...)
-2*dBCT(y,mu,sigma,nu,tau,log=TRUE),
rqres = expression(rqres(pfun="pBCT", type="Continuous", y=y, mu=mu, sigma=sigma, nu=nu, tau=tau)) ,
mu.initial = expression(mu <- (y+mean(y))/2),
sigma.initial = expression(sigma<- rep(0.1, length(y))),
nu.initial = expression(nu <- rep(0.5, length(y))),
tau.initial = expression(tau <-rep(10, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) TRUE ,
tau.valid = function(tau) all(tau > 0),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family","family"))
}
#-----------------------------------------------------------------
dBCT <- dBCTo <- function(x, mu=5, sigma=0.1, nu=1, tau=2, log=FALSE)
{
if (any(mu <= 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau <= 0)) stop(paste("tau must be positive", "\n", ""))
# if (any(x < 0)) stop(paste("x must be positive", "\n", ""))
if(length(nu)>1) z <- ifelse(nu != 0,(((x/mu)^nu-1)/(nu*sigma)),log(x/mu)/sigma)
else if (nu != 0) z <- (((x/mu)^nu-1)/(nu*sigma)) else z <- log(x/mu)/sigma
loglik <- (nu-1)*log(x)-nu*log(mu)-log(sigma)
fTz <- lgamma((tau+1)/2)-lgamma(tau/2)-0.5*log(tau)-lgamma(0.5)
fTz <- fTz-((tau+1)/2)* log(1+(z*z)/tau)
loglik <- loglik+fTz-log(pt(1/(sigma*abs(nu)),df=tau))
if (length(tau)>1) loglik <- ifelse(tau>1000000, dBCCG(x,mu,sigma,nu,log=TRUE), loglik) # MS Wednesday, April 12, 2006
else if (tau>1000000) loglik <- dBCCG(x,mu,sigma,nu,log=TRUE)
ft <- if(log==FALSE) exp(loglik) else loglik
ft <-ifelse(x <= 0, 0, ft)
ft
}
#-----------------------------------------------------------------
pBCT <- pBCTo <- function(q, mu=5, sigma=0.1, nu=1, tau=2, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu < 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau < 0)) stop(paste("tau must be positive", "\n", ""))
# if (any(q < 0)) stop(paste("y must be positive", "\n", ""))
if(length(nu)>1) z <- ifelse(nu != 0,(((q/mu)^nu-1)/(nu*sigma)),log(q/mu)/sigma)
else if (nu != 0) z <- (((q/mu)^nu-1)/(nu*sigma)) else z <- log(q/mu)/sigma
FYy1 <- pt(z,tau)
if(length(nu)>1) FYy2 <- ifelse(nu > 0, pt(-1/(sigma*abs(nu)),df=tau) ,0)
else if (nu>0) FYy2 <- pt(-1/(sigma*abs(nu)),df=tau) else FYy2 <- 0
FYy3 <- pt(1/(sigma*abs(nu)),df=tau)
FYy <- (FYy1-FYy2)/FYy3
if(lower.tail==TRUE) FYy <- FYy else FYy <- 1-FYy
if(log.p==FALSE) FYy <- FYy else FYy<- log(FYy)
FYy <-ifelse(q <= 0, 0, FYy)
FYy
}
#-----------------------------------------------------------------
qBCT <- qBCTo <- function(p, mu=5, sigma=0.1, nu=1, tau=2, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu < 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau < 0)) stop(paste("tau must be positive", "\n", ""))
if (log.p==TRUE) p <- exp(p) else p <- p
if (any(p <= 0)|any(p >= 1)) stop(paste("p must be between 0 and 1", "\n", ""))
if (lower.tail==TRUE) p <- p else p <- 1-p
if(length(nu)>1)
{
z <- ifelse((nu<=0),qt(p*pt(1/(sigma*abs(nu)),tau),tau),qt(1-(1-p)*pt(1/(sigma*abs(nu)),tau),tau))
}
else {
z <- if (nu<=0) qt(p*pt(1/(sigma*abs(nu)),tau),tau)
else qt(1-(1-p)*pt(1/(sigma*abs(nu)),tau),tau)
}
if(length(nu)>1) ya <- ifelse(nu != 0,mu*(nu*sigma*z+1)^(1/nu),mu*exp(sigma*z))
else if (nu != 0) ya <- mu*(nu*sigma*z+1)^(1/nu) else ya <- mu*exp(sigma*z)
ya
}
#-----------------------------------------------------------------
rBCT <- rBCTo <- function(n, mu=5, sigma=0.1, nu=1, tau=2)
{
if (any(mu <= 0)) stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0)) stop(paste("sigma must be positive", "\n", ""))
if (any(tau <= 0)) stop(paste("tau must be positive", "\n", ""))
if (any(n <= 0)) stop(paste("n must be a positive integer", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qBCT(p,mu=mu,sigma=sigma,nu=nu,tau=tau)
r
}
#-----------------------------------------------------------------
BCTuntr <- function (mu.link="identity", sigma.link="log", nu.link ="identity", tau.link="log")
{
mstats <- checklink("mu.link", "Box Cox t ", substitute(mu.link), c("1/mu^2", "log", "identity"))
dstats <- checklink("sigma.link", "Box Cox t ", substitute(sigma.link), c("inverse", "log", "identity"))
vstats <- checklink("nu.link", "Box Cox t ",substitute(nu.link), c("1/nu^2", "log", "identity"))
tstats <- checklink("tau.link", "Box Cox t ",substitute(tau.link), c("1/tau^2", "log", "identity"))
structure(
list(family = c("BCTuntr", "Box-Cox t untrucated"),
parameters = list(mu=TRUE, sigma=TRUE, nu=TRUE, tau=TRUE),
nopar = 4,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
tau.link = as.character(substitute(tau.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
tau.linkfun = tstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
tau.linkinv = tstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
tau.dr = tstats$mu.eta,
dldm = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
dldm <- k*u*(z/mu)+(nu/mu)*(u*(z*z)-1)
dldm
},
d2ldm2 = function(mu,sigma,nu,tau){
d2ldm2 <- -(tau+2*nu*nu*sigma*sigma*tau+1)/(tau+3)
d2ldm2 <- d2ldm2/(mu*mu*sigma*sigma)
},
dldd = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
dldd <- k*(u*(z*z)-1)
dldd
} ,
d2ldd2 = function(sigma,tau) -2*tau/(sigma^2*(tau+3)),
dldv = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
lnybym <- log(y/mu)
dldv <- ((u*z)/nu)*(z-(lnybym*k))
dldv <- dldv-lnybym*(u*z*z-1)
} ,
d2ldv2 = function(sigma) {
-7*(sigma^2)/4
},
dldt = function(y,mu,sigma,nu,tau) {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z+ifelse(nu == 0,1,0)*log(y/mu)*k
u <- (tau+1)/(tau+z^2)
#t2 <- tau/2
#t3 <- (tau+1)/2
dldt <- -0.5*log(1+(z*z)/tau)+0.5*u*(z*z)/tau
dldt <- dldt+0.5*digamma((tau+1)/2)-0.5*digamma(tau/2)-1/(2*tau)
} ,
d2ldt2 = function(tau) {
t2 <- tau/2
t3 <- (tau+1)/2
d2ldt2 <- trigamma(t3) -trigamma(t2) +2*(tau+5)/(tau*(tau+1)*(tau+3))
d2ldt2 <- d2ldt2/4
d2ldt2 <- ifelse(d2ldt2 < -1e-15, d2ldt2,-1e-15)
d2ldt2
} ,
d2ldmdd = function(mu,sigma,nu,tau) -(2*nu*tau)/(mu*sigma*(tau+3)),
d2ldmdv = function(mu,tau) (tau-3)/(2*mu*(tau+3)),
d2ldmdt = function(mu,nu,tau) (2*nu)/(mu*(tau+1)*(tau+3)),
d2ldddv = function(sigma,nu,tau) -(sigma*nu*tau)/(tau+3),
d2ldddt = function(sigma,tau) 2/(sigma*(tau+1)*(tau+3)),
d2ldvdt = function(sigma,nu,tau) (2*sigma^2*nu)/(tau^2),
G.dev.incr = function(y,mu,sigma,nu,tau,...) {
tf <- pt(1/(sigma*abs(nu)),tau)
if(any(tf<.99))
warning(paste("The truncation factor F(1/(sigma*|nu|)) \n",
"of BCT is less than 0.99 for some observations",
"\n"))
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z + ifelse(nu == 0,1,0)*log(y/mu)*k
lik <- (nu*log(y/mu)-log(y)+log(k))
lik <- lik+lgamma((tau+1)/2)-lgamma(tau/2)-0.5*log(tau)-lgamma(0.5)
lik <- lik-((tau+1)/2)* log(1+(z*z)/tau)
G.dev.incr <- -2*lik
G.dev.incr
} ,
rqres =expression( {
k <- 1/sigma
z <- ifelse(nu != 0,1,0)*(((y/mu)^nu-1)*(k/nu))
z <- z + ifelse(nu == 0,1,0)*log(y/mu)*k
rqres <- qnorm(pt(z,tau))
}) ,
mu.initial = expression(mu <- y),
sigma.initial = expression(sigma<- rep(0.1, length(y))),
nu.initial = expression(nu <- rep(0.5, length(y))),
tau.initial = expression(tau <-rep(10, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) TRUE ,
tau.valid = function(tau) all(tau > 0),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family","family"))
}
#-----------------------------------------------------------------------------------------
BCTo <- function (mu.link="log", sigma.link="log", nu.link ="identity", tau.link="log")
{
mstats <- checklink("mu.link", "Box Cox t ", substitute(mu.link),
c("inverse", "log", "identity", "own"))
dstats <- checklink("sigma.link", "Box Cox t ", substitute(sigma.link),
c("inverse", "log", "identity", "own"))
vstats <- checklink("nu.link", "Box Cox t ",substitute(nu.link),
c("inverse", "log", "identity", "own"))
tstats <- checklink("tau.link", "Box Cox t ",substitute(tau.link),
c("inverse", "log", "identity", "own"))
structure(
list(family = c("BCTo", "Box-Cox-t-orig."),
parameters = list(mu=TRUE, sigma=TRUE, nu=TRUE, tau=TRUE),
nopar = 4,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
tau.link = as.character(substitute(tau.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
tau.linkfun = tstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
tau.linkinv = tstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
tau.dr = tstats$mu.eta,
dldm = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
dldm <- (w*z)/(mu*sigma)+(nu/mu)*(w*(z^2)-1)
dldm
},
d2ldm2 = function(mu,sigma,nu,tau){
d2ldm2 <- -(tau+2*nu*nu*sigma*sigma*tau+1)/(tau+3)
d2ldm2 <- d2ldm2/(mu*mu*sigma*sigma)
},
dldd = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldd <- (w*(z^2)-1)/sigma + h/(sigma^2*abs(nu))
dldd
} ,
d2ldd2 = function(sigma, tau) -2*tau/(sigma^2*(tau+3)),
dldv = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
h <- dt(1/(sigma*abs(nu)),df=tau)/pt(1/(sigma*abs(nu)),df=tau)
dldv <- ((w*z^2)/nu)-log(y/mu) *(w*z^2+((w*z)/(sigma*nu))-1)
dldv <- dldv+sign(nu)*h/(sigma*nu^2)
} ,
d2ldv2 = function(sigma) {
-7*(sigma^2)/4
},
dldt = function(y,mu,sigma,nu,tau) {
z <- ifelse(nu != 0,(((y/mu)^nu-1)/(nu*sigma)),log(y/mu)/sigma)
w <- (tau+1)/(tau+z^2)
j <- (log(pt(1/(sigma*abs(nu)),df=tau+0.01))
-log(pt(1/(sigma*abs(nu)),df=tau)))/0.01
dldt <- -0.5*log(1+(z^2)/tau)+(w*(z^2))/(2*tau)
dldt <- dldt+0.5*digamma((tau+1)/2)-0.5*digamma(tau/2)-1/(2*tau)-j
} ,
d2ldt2 = function(tau) {
d2ldt2 <- trigamma((tau+1)/2) -trigamma(tau/2) +2*(tau+5)/(tau*(tau+1)*(tau+3))
d2ldt2 <- d2ldt2/4
d2ldt2 <- ifelse(d2ldt2 < -1e-15, d2ldt2,-1e-15)
d2ldt2
} ,
d2ldmdd = function(mu,sigma,nu,tau) -(2*nu*tau)/(mu*sigma*(tau+3)),
d2ldmdv = function(mu,tau) (tau-3)/(2*mu*(tau+3)),
d2ldmdt = function(mu,nu,tau) (2*nu)/(mu*(tau+1)*(tau+3)),
d2ldddv = function(sigma,nu,tau) -(sigma*nu*tau)/(tau+3),
d2ldddt = function(sigma,tau) 2/(sigma*(tau+1)*(tau+3)),
d2ldvdt = function(sigma,nu,tau) (2*sigma^2*nu)/(tau^2),
G.dev.incr = function(y,mu,sigma,nu,tau,...)
-2*dBCTo(y,mu,sigma,nu,tau,log=TRUE),
rqres = expression(rqres(pfun="pBCTo", type="Continuous", y=y, mu=mu, sigma=sigma, nu=nu, tau=tau)) ,
mu.initial = expression(mu <- (y+mean(y))/2),
sigma.initial = expression(sigma<- rep(0.1, length(y))),
nu.initial = expression(nu <- rep(0.5, length(y))),
tau.initial = expression(tau <-rep(10, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) TRUE ,
tau.valid = function(tau) all(tau > 0),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family","family"))
}
#------------------------------------------------------------------------
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.