ddweibull: The Discrete Weibull Distribution (Type 1)

In BDgraph: Bayesian Structure Learning in Graphical Models using Birth-Death MCMC

The Discrete Weibull Distribution (Type 1)

Description

Density, distribution function, quantile function and random generation for the discrete Weibull distribution (type I) with parameters q and \beta.

Usage

ddweibull(x, q = exp(-1), beta = 1, zero = TRUE)
pdweibull(x, q = exp(-1), beta = 1, zero = TRUE)
qdweibull(p, q = exp(-1), beta = 1, zero = TRUE)
rdweibull(n, q = exp(-1), beta = 1, zero = TRUE)

Arguments

x	vector of quantiles.
p	vector of probabilities.
q, beta	shape and scale parameters, the latter defaulting to 1.
zero	logical; if TRUE (default), the support contains 0; FALSE otherwise.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The discrete Weibull distribution has density given by

f(x) = q^{x^\beta} - q^{(x+1)^\beta}, x = 0, 1, 2, \ldots

For the case zero = FALSE:

f(x) = q^{(x-1)^\beta} - q^{x^\beta}, x = 1, 2, \ldots

Cumulative distribution function

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

For the case zero = FALSE, x+1 should replaced by x.

Value

ddweibull gives the density, pdweibull gives the distribution function, qdweibull gives the quantile function, and rdweibull generates random values.

Author(s)

Reza Mohammadi [e-mail], Pariya Behrouzi, Veronica Vinciotti

References

Nakagawa, T. and Osaki, S. (1975). The Discrete Weibull Distribution. IEEE Transactions on Reliability, R-24, 300-301, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1109/TR.1975.5214915")}

See Also

dweibull, bdw.reg, bdgraph.dw

Examples

n    = 1000
q    = 0.4
beta = 0.8

set.seed(7)

rdw = rdweibull(n = n, q = q, beta = beta)

plot(prop.table(table(rdw)), type = "h", col = "gray50")

x = 0:max(rdw)

lines(x, ddweibull(x = x, q = q, beta = beta), type = "o", col = "blue", lwd = 2)

hist(pdweibull(x = rdw, q = q, beta = beta))

plot(ecdf(rdw))
lines(x, pdweibull(x, q = q, beta = beta), col = "blue", lwd = 2, type = "s")

BDgraph documentation built on Aug. 29, 2025, 5:16 p.m.