pZABS: Zero Adjusted Birnbaum-Saunders (ZABS) distribution for...

In santosneto/rbsmodels: Reparameterized Birnbaum-Saunders regression model

Description

The fuction ZABS() defines the ZABS distribution, a two paramenter distribution, for a gamlss.family object to be used in GAMLSS fitting using using the function 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)

Arguments

mu	vector of scale parameter values
sigma	vector of shape parameter values
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
mu.link	object for which the extraction of model residuals is meaningful.
sigma.link	type of residual to be used.
x, q	vector of quantiles
log,	log.p logical; if TRUE, probabilities p are given as log(p).
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
from	where to start plotting the distribution from
to	up to where to plot the distribution
obj	a fitted RBS object
...	other graphical parameters for plotting

Details

The parametrization of the normal distribution given in the function ZABS() is

f_{Y}(y;μ,δ,p) =\frac{[1-p]√{δ+1}}{4\,y^{3/2}\,√{πμ}}≤ft[y+\frac{δμ}{δ+1} \right]\exp≤ft(-\frac{δ}{4}≤ft[\frac{y[δ+1]}{δμ}+\frac{δμ}{y[δ+1]}-2\right]\right) I_{(0, ∞)}(y)+ pI_{\{0\}}(y).

Value

returns a gamlss.family object which can be used to fit a normal distribution in the gamlss() function.

Note

For the function ZABS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.

Author(s)

Manoel Santos-Neto [e-mail], F.J.A. Cysneiros [e-mail], Victor Leiva [e-mail] and Michelli Barros [e-mail]

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. Applied Stochastic Models in Business and Industry. 10.1002/asmb.2124.

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)

santosneto/rbsmodels documentation built on May 29, 2019, 1:49 p.m.