descriptive.zmpl: Zero Modified Poisson-Lindley (ZMPL) distribution

In zmpldistribution/zmpl: Zero Modified Poisson-Lindley distribution

Description

The fuction ZMPL() defines the ZMPL distribution, a two paramenter distribution. The zero modified Poisson-Lindley distribution is similar to the Poisson-Lindley distribution but allows zeros as y values. The extra parameter models the probabilities at zero. The functions dZMPL, pZMPL, qZMPL and rZMPL define the density, distribution function, quantile function and random generation for the zero modified Poisson-Lindley distribution. plotZMPL can be used to plot the distribution. meanZMPL calculates the expected value of the response for a fitted model.

Usage

dZMPL(x, mu = 1, sigma = 1, nu=0.1, log = FALSE)
pZMPL(q, mu = 1, sigma = 1,  nu=0.1, lower.tail = TRUE, log.p = FALSE)
qZMPL(p, mu = 1, sigma = 1,  nu=0.1, lower.tail = TRUE, log.p = FALSE)
rZMPL(n, mu = 1, sigma = 1)
plotZMPL(mu = .5, sigma = 1,  nu=0.1, from = 0, to = 0.999, n = 101, ...)
meanZMPL(obj)

Arguments

x, q	vector of observations/quantiles
mu	vector of scale parameter values
sigma	vector of shape parameter values
log,	log.p logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
p	vector of probabilities.
n	number of observations. If 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
...	other graphical parameters for plotting

Details

The probability massa function of the is given by

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 object of the ZMPL distribution.

Note

For the function ZMPL(), mu is the mean and sigma is the precision parameter and nu is the proportion of zeros of the zero adjusted 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

plotZARBS()
dat <- rZARBS(1000); hist(dat)
fit <- gamlss(dat~1,family=ZARBS(),method=CG())
meanZABS(fit)

data(papatoes);
fit = gamlss(I(Demand/10000)~1,sigma.formula=~1, nu.formula=~1, family=ZARBS(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=ZARBS(mu.link="identity",sigma.link = "identity",nu.link = "identity"),method=CG(),data=oil)
summary(fit1)

zmpldistribution/zmpl documentation built on May 11, 2019, 5:16 p.m.