DWreg (version 1.0)

dw: 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

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.

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.

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")