fi.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, theta = 1, p0=0.1, log = FALSE)
pZMPL(q, theta = 1, p0=0.1, lower.tail = TRUE, log.p = FALSE)
qZMPL(p, theta = 1, p0=0.1, lower.tail = TRUE, log.p = FALSE)
rZMPL(n, theta = 1, p0=0.1)
plotZMPL(theta = 1, p0=0.1, from = 0, to = 0.999, n = 101, ...)
meanZMPL(obj)

Arguments

theta	theta parameter values
p0	p0 parameter values
x, q	vector of observations/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.
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_{X}(x;θ,p0) = p0 + (1-p0)*P[Y=0] I(y=0) + (1-p0)*P[Y>0] I(y>0)

where

P[Y=y]

is a probability massa function of the Poisson-Lindley distribution.

Author(s)

Manoel Santos-Neto [e-mail], Marcelo Bourguignon [e-mail], Danillo Xavier [e-mail] and Vera Tomazella [e-mail]

References

Bourguignon, M., Xavier, D., Santos-Neto, M., Tomazella, V. (2017) The Modified Poisson-Lindley distribution: A model for overdispersed and underdispersed count data. manuscript.

Examples

FIZMPL()
theta <- seq(0.05,1,l=100)
aux0 <- - ((theta^2)*(theta+2)/( (theta^2) +3*theta+1) )
p0 <- seq(0,1,l=100)
g <- expand.grid(x = theta, y = p0)
z <- FIZMPL(theta,p0)
z[z<0] <- 0
g$z <- z
print(wireframe(z ~ x * y  ,g, xlab=expression(theta), scales = list(arrows = FALSE), ylab=expression(pi), zlab = "FI(X)") )


theta <- seq(0.05,1,l=100)
aux0 <- - ((theta^2)*(theta+2)/( (theta^2) +3*theta+1) )
p0 <- seq(min(aux0),0,l=100)
g <- expand.grid(x = theta, y = p0)
z <- FIZMPL(theta,p0)
z[z<0] <- 0
g$z <- z
print(wireframe(z ~ x * y  ,g, xlab=expression(theta), scales = list(arrows = FALSE), ylab=expression(pi), zlab = "FI(X)") )

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