qzmpl: Zero Modified Poisson-Lindley (ZMPL) distribution

In zmpldistribution/zmpl: Zero Modified Poisson-Lindley distribution

Description

Density, distribution function, quantile function and random generation for the ZMPL distribution.

Usage

dzmpl(x, theta,  p0 = 0, log = FALSE)
pzmpl(q, theta = 5, p0 = 0, lower.tail = TRUE, log.p = FALSE)
qzmpl(p, theta = 5, p0 = 0, lower.tail = TRUE, log.p = FALSE)
rzmpl(n, theta = 5, p0 = 0)

Arguments

p	vector of probabilities.
theta	vector of scale parameter values
p0	vector of shape parameter values
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
x, q	vector of observations/quantiles
log,	log.p logical; if TRUE, probabilities p are given as log(p).
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

If theta or p0 not specified they assume the default values of 5 and 0, respectively.

The ZMPL distribution has density:

Pr(X=k)=≤ft\{\begin{array}{ll} π + (1 - π)\frac{θ^2(θ + 2)}{(θ + 1)^3},&k = 0, \\&\\(1 - π)\frac{θ^2(k + θ + 2)}{(θ + 1)^{k+3}},&k \in \mathbb{N}^{ {\tiny +}}. \end{array}\right.

Value

returns a object of the ZMPL distribution.

Note

For the function ZMPL(), p0 is the zero-modification parameter and different values lead to different modifications of the ZMPL distribution.

Author(s)

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

References

Santos-Neto, M., Xavier, D., Bourguignon, M. and Tomazella, V. (2017) Zero-Modified Poisson-Lindley distribution with applications in inflated and deflated of zeros. to appear.

Examples

dat <- rzmpl(1000); plot(table(dat),type="h",xlab="x",ylab="PMF")
fit <- fitzmpl(dat)

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