dw: Discrete Weibull

In DWreg: Parametric Regression for Discrete Response

Discrete Weibull

Description

Density, distribution function, quantile function and random generation for the discrete Weibull distribution with parameters q and beta.

Usage

ddw(x,q=exp(-1),beta=1)
pdw(x,q=exp(-1),beta=1)
qdw(p,q=exp(-1),beta=1)
rdw(n,q=exp(-1),beta=1)

Arguments

x	quantile
p	probability
n	number of observations
q, beta	Parameters of the distribution

Details

The discrete Weibulll distribution has density

p(x,q,\beta) = q^{x^{\beta}}-q^{(x+1)^{\beta}}

for x = 0, 1, 2, \ldots. If q or beta are not specified they assume the default values of exp(-1) and 1, respectively. In this case, DW corresponds to a geometric distribution with p=1-q.

Value

ddw gives the density, pdw gives the distribution function, qdw gives the quantile function, and rdw generates random samples from a DW distribution with parameters q and beta.

Author(s)

Veronica Vinciotti

References

Nagakawa T, Osaki S. The discrete Weibull distribution. IEEE transactions on reliability 1975; R-24(5).

Examples

x<-rdw(1000,q=0.9,beta=1.5)
hist(x)
plot(x,unlist(lapply(x,ddw,q=0.9,beta=1.5)),ylab="density")
plot(x,unlist(lapply(x,pdw,q=0.9,beta=1.5)),ylab="cdf")

DWreg documentation built on June 8, 2025, 10:20 a.m.