R/ZIRBS.R
In santosneto/rbsmodels: Reparameterized Birnbaum-Saunders regression model
Defines functions
esp1
dZABS
pZABS
Documented in
dZABS
esp1
pZABS
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the zero adjusted Birnbaum-Saunders distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter and nu is the proportion of zeros of the zero adjusted Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'
#'@export
#'
ZABS <- function (mu.link = "log", sigma.link = "log", nu.link = "logit")
{
mstats = checklink("mu.link", "ZABS", substitute(mu.link),
c("sqrt", "log", "identity"))
dstats = checklink("sigma.link", "ZABS", substitute(sigma.link),
c("sqrt", "log", "identity"))
vstats = checklink("nu.link", "ZABS", substitute(nu.link),
c("logit", "probit", "cloglog", "log", "own"))
structure(list(family = c("ZABS", "Zero-Adjusted Birnbaum-Saunders"),
parameters = list(mu = TRUE, sigma = TRUE, nu = TRUE),
nopar = 3,
type = "Mixed",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
dldm = function(y,mu,sigma) #first derivate of log-density respect to mu
{
mustart = 1/(2*mu)
ystart = ((sigma+1)*y)/(4*mu*mu) - (sigma^2)/(4*(sigma+1)*y) + (sigma/(sigma+1))*(1/( y + ((mu*sigma)/(sigma+1)) ))
dldm <- ifelse((y == 0) , 0, ystart - mustart)
dldm
},
d2ldm2 = function(y,mu,sigma) { #expected of second derivate of log-density respect to mu
Ims = mapply(esp1,mu,sigma)
d2ldm2 = ifelse((y == 0) , 0, - sigma/(2*mu*mu) - ((sigma/(sigma+1))^2)*Ims )
d2ldm2
},
dldd = function(y,mu,sigma) { #first derivate log-density respect to sigma
sigmastart = -(sigma+2)/(2*(sigma+1))
ystart.sigma = (mu/((sigma+1)^2))*(1/( y + ((mu*sigma)/(sigma+1)) )) - y/(4*mu) - (mu*sigma*(sigma+2))/(4*y*((sigma+1)^2))
dldd = ifelse((y==0),0,(ystart.sigma - sigmastart))
dldd
},
d2ldd2 = function(y,mu,sigma) { #expected of second derivate log-density respect to sigma
Ims = mapply(esp1,mu,sigma)
lss = ((sigma^2) + 3*sigma + 1)/(2*((sigma+1)^2)*(sigma^2))
d2ldd2 <- ifelse((y==0),0, -lss - ((mu^2)/((sigma+1)^4))*Ims)
d2ldd2
},
dldv = function(y,nu) { #first derivate log-density respect to nu
dldv <- ifelse(y == 0, 1/nu, -1/(1 - nu))
dldv
},
d2ldv2 = function(nu) { #expected of second derivate log-density respect to nu
d2ldv2 <- -1/(nu * (1 - nu))
d2ldv2
},
d2ldmdd = function(y,mu,sigma) { #expected of partial derivate of log-density respect to mu and sigma
Ims = mapply(esp1,mu,sigma)
lms = 1/(2*mu*(sigma+1))
d2ldmdd <- ifelse((y == 0), 0, - lms - ((mu*sigma)/((sigma+1)^3))*Ims )
d2ldmdd
},
d2ldmdv = function(y) { #partial derivate of log-density respect to mu and nu
d2ldmdv <- rep(0,length(y))
d2ldmdv
},
d2ldddv = function(y) { #partial derivate of log-density respect to sigma and nu
d2ldddv <- rep(0,length(y))
d2ldddv
},
G.dev.incr = function(y, mu, sigma, nu, ...){ # Global deviance
-2 * dZABS(y, mu, sigma, nu, log = TRUE)
},
rqres = expression({ # (Normalize quantile) residuals
uval <- ifelse(y == 0, nu * runif(length(y), 0, 1),
(1 - nu) * pZABS(y, mu, sigma, nu))
rqres <- qnorm(uval)
}),
mu.initial = expression(mu <- mean(y[y>0])),
sigma.initial = expression(sigma <- rep(1, length(y))),
nu.initial = expression(nu <- rep(0.3, length(y))),
mu.valid = function(mu) TRUE,
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) all(nu > 0) && all(nu < 1),
y.valid = function(y) all(y >= 0)),
class = c("gamlss.family", "family"))
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the zero adjusted Birnbaum-Saunders distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter and nu is the proportion of zeros of the zero adjusted Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'
#'@export
#'
esp1 <- function(mu=1,sigma=1)
{
a <- sqrt(2/sigma)
b <- (mu*sigma)/(sigma+1)
E <- function(x)(1/((x+b)^2))*dcbs(x,alpha=a,beta=b)
return(integrate(E,0,Inf)$value)
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5,sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
dZABS<-function(x, mu=1, sigma=1, nu=.1, log=FALSE)
{
if (any(mu < 0) || any(is.na(mu))) stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0) || any(is.na(sigma))) stop(paste("sigma must be positive", "\n", ""))
if (any(x < 0)) stop(paste("x must be positive", "\n", ""))
log.lik <- ifelse(x==0, log(nu), log(1-nu) + 0.5*(sigma - log(mu) + log(sigma+1) - log(16*pi)) - (3/2)*log(x) - ((sigma+1)/(4*mu))*x - ((mu*sigma*sigma)/(4*(sigma+1)))*(1/x) + log(x + ((mu*sigma)/(sigma+1))))
if(log==FALSE) fy <- exp(log.lik) else fy <- log.lik
fy
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
pZABS <- function(q, mu=1, sigma=1, nu=0.1, 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(q < 0)) stop(paste("y must be positive", "\n", ""))
a <- sqrt(2/sigma)
b <- (mu*sigma)/(sigma+1)
cdf1 <- pnorm((1/a)*(sqrt(q/b) - sqrt(b/q)))
cdf <- cdf1
## the problem with this approximation is that it is not working with
## small sigmas and produce NA's. So here it is a solution
if (any(is.na(cdf)))
{
index <- seq(along=q)[is.na(cdf)]
for (i in index)
{
cdf[i] <- integrate(function(x)
dcbs(x, alpha = a[i], beta = b[i], log=FALSE), 0.001, q[i] )$value
}
}
cdf <- ifelse((q==0), nu, nu+(1-nu)*cdf)
if(lower.tail==TRUE) cdf <- cdf else cdf <- 1-cdf
if(log.p==FALSE) cdf <- cdf else cdf <- log(cdf)
cdf
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
qZABS <- function (p, mu = 0.5, sigma = 1, nu = 0.1, lower.tail = TRUE,
log.p = FALSE)
{
if (any(mu <= 0))
stop(paste("mu must be positive ", "\n", ""))
if (any(sigma < 0)) #In this parametrization sigma = delta
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0)|any(nu >= 1)) #In this parametrization nu = p
stop(paste("nu must be beetwen 0 and 1 ", "\n", ""))
if (log.p == TRUE)
p <- exp(p)
else p <- p
if (lower.tail == TRUE)
p <- p
else p <- 1 - p
if (any(p < 0) | any(p > 1))
stop(paste("p must be between 0 and 1", "\n", ""))
a <- sqrt(2/sigma)
b <- (mu*sigma)/(sigma+1)
suppressWarnings(q <- ifelse((nu >= p),0, qcbs((p - nu)/(1-nu),alpha = a, beta = b, lower.tail = TRUE, log.p = FALSE)))
q
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
rZABS <- function (n, mu = 0.5, sigma = 1, nu = 0.1)
{
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0)) #In this parametrization sigma = delta
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0)|any(nu >= 1)) #In this parametrization nu = p
stop(paste("nu must be beetwen 0 and 1 ", "\n", ""))
if (any(n <= 0))
stop(paste("n must be a positive integer", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qZABS(p, mu = mu, sigma = sigma, nu = nu)
r
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
plotZABS = function (mu = .5, sigma = 1, nu = 0.1, from = 0, to = 0.999, n = 101, title="title",
...)
{
y <- seq(from = 0.001, to = to, length.out = n)
pdf <- dZABS(y, mu = mu, sigma = sigma, nu = nu)
pr0 <- c(dZABS(0, mu = mu, sigma = sigma, nu = nu))
po <- c(0)
plot(pdf ~ y, main=title, ylim = c(0, max(pdf,pr0)), type = "l",lwd=3)
points(po, pr0, type = "h",lwd=3)
points(po, pr0, type = "p", col = "red",lwd=3)
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
meanZABS <- function (obj)
{
if (obj$family[1] != "ZABS")
stop("the object do not have a ZABS distribution")
meanofY <- (1 - fitted(obj, "nu")) * fitted(obj, "mu")
meanofY
}
santosneto/rbsmodels documentation built on May 29, 2019, 1:49 p.m.
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Defines functions esp1 dZABS pZABS
Documented in dZABS esp1 pZABS
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the zero adjusted Birnbaum-Saunders distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter and nu is the proportion of zeros of the zero adjusted Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'
#'@export
#'
ZABS <- function (mu.link = "log", sigma.link = "log", nu.link = "logit")
{
mstats = checklink("mu.link", "ZABS", substitute(mu.link),
c("sqrt", "log", "identity"))
dstats = checklink("sigma.link", "ZABS", substitute(sigma.link),
c("sqrt", "log", "identity"))
vstats = checklink("nu.link", "ZABS", substitute(nu.link),
c("logit", "probit", "cloglog", "log", "own"))
structure(list(family = c("ZABS", "Zero-Adjusted Birnbaum-Saunders"),
parameters = list(mu = TRUE, sigma = TRUE, nu = TRUE),
nopar = 3,
type = "Mixed",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
dldm = function(y,mu,sigma) #first derivate of log-density respect to mu
{
mustart = 1/(2*mu)
ystart = ((sigma+1)*y)/(4*mu*mu) - (sigma^2)/(4*(sigma+1)*y) + (sigma/(sigma+1))*(1/( y + ((mu*sigma)/(sigma+1)) ))
dldm <- ifelse((y == 0) , 0, ystart - mustart)
dldm
},
d2ldm2 = function(y,mu,sigma) { #expected of second derivate of log-density respect to mu
Ims = mapply(esp1,mu,sigma)
d2ldm2 = ifelse((y == 0) , 0, - sigma/(2*mu*mu) - ((sigma/(sigma+1))^2)*Ims )
d2ldm2
},
dldd = function(y,mu,sigma) { #first derivate log-density respect to sigma
sigmastart = -(sigma+2)/(2*(sigma+1))
ystart.sigma = (mu/((sigma+1)^2))*(1/( y + ((mu*sigma)/(sigma+1)) )) - y/(4*mu) - (mu*sigma*(sigma+2))/(4*y*((sigma+1)^2))
dldd = ifelse((y==0),0,(ystart.sigma - sigmastart))
dldd
},
d2ldd2 = function(y,mu,sigma) { #expected of second derivate log-density respect to sigma
Ims = mapply(esp1,mu,sigma)
lss = ((sigma^2) + 3*sigma + 1)/(2*((sigma+1)^2)*(sigma^2))
d2ldd2 <- ifelse((y==0),0, -lss - ((mu^2)/((sigma+1)^4))*Ims)
d2ldd2
},
dldv = function(y,nu) { #first derivate log-density respect to nu
dldv <- ifelse(y == 0, 1/nu, -1/(1 - nu))
dldv
},
d2ldv2 = function(nu) { #expected of second derivate log-density respect to nu
d2ldv2 <- -1/(nu * (1 - nu))
d2ldv2
},
d2ldmdd = function(y,mu,sigma) { #expected of partial derivate of log-density respect to mu and sigma
Ims = mapply(esp1,mu,sigma)
lms = 1/(2*mu*(sigma+1))
d2ldmdd <- ifelse((y == 0), 0, - lms - ((mu*sigma)/((sigma+1)^3))*Ims )
d2ldmdd
},
d2ldmdv = function(y) { #partial derivate of log-density respect to mu and nu
d2ldmdv <- rep(0,length(y))
d2ldmdv
},
d2ldddv = function(y) { #partial derivate of log-density respect to sigma and nu
d2ldddv <- rep(0,length(y))
d2ldddv
},
G.dev.incr = function(y, mu, sigma, nu, ...){ # Global deviance
-2 * dZABS(y, mu, sigma, nu, log = TRUE)
},
rqres = expression({ # (Normalize quantile) residuals
uval <- ifelse(y == 0, nu * runif(length(y), 0, 1),
(1 - nu) * pZABS(y, mu, sigma, nu))
rqres <- qnorm(uval)
}),
mu.initial = expression(mu <- mean(y[y>0])),
sigma.initial = expression(sigma <- rep(1, length(y))),
nu.initial = expression(nu <- rep(0.3, length(y))),
mu.valid = function(mu) TRUE,
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) all(nu > 0) && all(nu < 1),
y.valid = function(y) all(y >= 0)),
class = c("gamlss.family", "family"))
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the zero adjusted Birnbaum-Saunders distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter and nu is the proportion of zeros of the zero adjusted Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'
#'@export
#'
esp1 <- function(mu=1,sigma=1)
{
a <- sqrt(2/sigma)
b <- (mu*sigma)/(sigma+1)
E <- function(x)(1/((x+b)^2))*dcbs(x,alpha=a,beta=b)
return(integrate(E,0,Inf)$value)
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5,sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
dZABS<-function(x, mu=1, sigma=1, nu=.1, log=FALSE)
{
if (any(mu < 0) || any(is.na(mu))) stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0) || any(is.na(sigma))) stop(paste("sigma must be positive", "\n", ""))
if (any(x < 0)) stop(paste("x must be positive", "\n", ""))
log.lik <- ifelse(x==0, log(nu), log(1-nu) + 0.5*(sigma - log(mu) + log(sigma+1) - log(16*pi)) - (3/2)*log(x) - ((sigma+1)/(4*mu))*x - ((mu*sigma*sigma)/(4*(sigma+1)))*(1/x) + log(x + ((mu*sigma)/(sigma+1))))
if(log==FALSE) fy <- exp(log.lik) else fy <- log.lik
fy
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
pZABS <- function(q, mu=1, sigma=1, nu=0.1, 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(q < 0)) stop(paste("y must be positive", "\n", ""))
a <- sqrt(2/sigma)
b <- (mu*sigma)/(sigma+1)
cdf1 <- pnorm((1/a)*(sqrt(q/b) - sqrt(b/q)))
cdf <- cdf1
## the problem with this approximation is that it is not working with
## small sigmas and produce NA's. So here it is a solution
if (any(is.na(cdf)))
{
index <- seq(along=q)[is.na(cdf)]
for (i in index)
{
cdf[i] <- integrate(function(x)
dcbs(x, alpha = a[i], beta = b[i], log=FALSE), 0.001, q[i] )$value
}
}
cdf <- ifelse((q==0), nu, nu+(1-nu)*cdf)
if(lower.tail==TRUE) cdf <- cdf else cdf <- 1-cdf
if(log.p==FALSE) cdf <- cdf else cdf <- log(cdf)
cdf
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
qZABS <- function (p, mu = 0.5, sigma = 1, nu = 0.1, lower.tail = TRUE,
log.p = FALSE)
{
if (any(mu <= 0))
stop(paste("mu must be positive ", "\n", ""))
if (any(sigma < 0)) #In this parametrization sigma = delta
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0)|any(nu >= 1)) #In this parametrization nu = p
stop(paste("nu must be beetwen 0 and 1 ", "\n", ""))
if (log.p == TRUE)
p <- exp(p)
else p <- p
if (lower.tail == TRUE)
p <- p
else p <- 1 - p
if (any(p < 0) | any(p > 1))
stop(paste("p must be between 0 and 1", "\n", ""))
a <- sqrt(2/sigma)
b <- (mu*sigma)/(sigma+1)
suppressWarnings(q <- ifelse((nu >= p),0, qcbs((p - nu)/(1-nu),alpha = a, beta = b, lower.tail = TRUE, log.p = FALSE)))
q
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
rZABS <- function (n, mu = 0.5, sigma = 1, nu = 0.1)
{
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0)) #In this parametrization sigma = delta
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0)|any(nu >= 1)) #In this parametrization nu = p
stop(paste("nu must be beetwen 0 and 1 ", "\n", ""))
if (any(n <= 0))
stop(paste("n must be a positive integer", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qZABS(p, mu = mu, sigma = sigma, nu = nu)
r
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
plotZABS = function (mu = .5, sigma = 1, nu = 0.1, from = 0, to = 0.999, n = 101, title="title",
...)
{
y <- seq(from = 0.001, to = to, length.out = n)
pdf <- dZABS(y, mu = mu, sigma = sigma, nu = nu)
pr0 <- c(dZABS(0, mu = mu, sigma = sigma, nu = nu))
po <- c(0)
plot(pdf ~ y, main=title, ylim = c(0, max(pdf,pr0)), type = "l",lwd=3)
points(po, pr0, type = "h",lwd=3)
points(po, pr0, type = "p", col = "red",lwd=3)
}
#'Zero Adjusted Birnbaum-Saunders (ZABS) distribution for fitting a GAMLSS
#'
#'@description The fuction \code{ZABS()} defines the ZABS distribution, a two paramenter
#'distribution, for a gamlss.family object to be used in GAMLSS fitting using using the
#'function \code{gamlss()}. The zero adjusted Birnbaum-Saunders distribution is similar
#'to the Birnbaum-Saunders distribution but allows zeros as y values. The extra parameter
#'models the probabilities at zero. The functions dZABS, pZABS, qZABS and rZABS define
#'the density, distribution function, quantile function and random generation for
#'the ZABS parameterization of the zero adjusted Birnbaum-Saunders distribution.
#'plotZABS can be used to plot the distribution. meanZABS calculates the expected
#'value of the response for a fitted model.
#'
#'@usage ZABS(mu.link = "identity", sigma.link = "identity")
#'dZABS(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
#'pZABS(q, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'qZABS(p, mu = 1, sigma = 1, nu=0.1, lower.tail = TRUE, log.p = FALSE)
#'rZABS(n, mu = 1, sigma = 1)
#'plotZABS(mu = .5, sigma = 1, nu=0.1, from = 0, to = 0.999, n = 101, ...)
#'meanRBS(obj)
#'
#' @param mu.link object for which the extraction of model residuals is meaningful.
#' @param sigma.link type of residual to be used.
#' @param x,q vector of quantiles
#' @param mu vector of scale parameter values
#' @param sigma vector of shape parameter values
#' @param log, log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param from where to start plotting the distribution from
#' @param to up to where to plot the distribution
#' @param obj a fitted RBS object
#' @param ... other graphical parameters for plotting
#'
#'
#' @details The parametrization of the normal distribution given in the function ZABS() is
#'
#'\deqn{ f_{Y}(y;\mu,\delta,p) =\frac{[1-p]\sqrt{\delta+1}}{4\,y^{3/2}\,\sqrt{\pi\mu}}\left[y+\frac{\delta\mu}{\delta+1} \right]\exp\left(-\frac{\delta}{4}\left[\frac{y[\delta+1]}{\delta\mu}+\frac{\delta\mu}{y[\delta+1]}-2\right]\right) I_{(0, \infty)}(y)+ pI_{\{0\}}(y).}
#'
#'@return returns a \code{gamlss.family} object which can be used to fit a normal distribution in the \code{gamlss()} function.
#'
#'@note For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.
#'
#'@references
#'Leiva, V., Santos-Neto, M., Cysneiros, F.J.A., Barros, M. (2015) A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution.
#'\emph{Applied Stochastic Models in Business and Industry.} \email{10.1002/asmb.2124}.
#'
#'@author
#'Manoel Santos-Neto \email{manoel.ferreira@ufcg.edu.br}, F.J.A. Cysneiros \email{cysneiros@de.ufpe.br}, Victor Leiva \email{victorleivasanchez@gmail.com} and Michelli Barros \email{michelli.karinne@gmail.com}
#'
#'@examples plotZABS()
#'dat <- rZABS(1000); hist(dat)
#'fit <- gamlss(dat~1,family=ZABS(),method=CG())
#'meanZABS(fit)
#'
#'data(papatoes);
#'fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=papatoes)
#'summary(fit)
#'
#'data(oil)
#'fit1 = gamlss(Demand~1,sigma.formula=~1, nu.formula=~1, family=ZABS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
#'summary(fit1)
#'@export
#'
meanZABS <- function (obj)
{
if (obj$family[1] != "ZABS")
stop("the object do not have a ZABS distribution")
meanofY <- (1 - fitted(obj, "nu")) * fitted(obj, "mu")
meanofY
}
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