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

Description Usage Arguments Details Value Note Author(s) References Examples

View source: R/ZIRBS.R

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

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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

from

where to start plotting the distribution from

to

up to where to plot the distribution

n

number of observations. If length(n) > 1, the length is taken to be the number required.

...

other graphical parameters for plotting

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).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

p

vector of probabilities.

obj

a fitted RBS object

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 [email protected], F.J.A. Cysneiros [email protected], Victor Leiva [email protected] and Michelli Barros [email protected]

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

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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 26, 2017, 12:32 a.m.