VGAM (version 0.8-3)

Betageom: The Beta-Geometric Distribution

Description

Density, distribution function, and random generation for the beta-geometric distribution.

Usage

dbetageom(x, shape1, shape2, log=FALSE)
pbetageom(q, shape1, shape2, log.p=FALSE)
rbetageom(n, shape1, shape2)

Arguments

x, q

vector of quantiles.

n

number of observations. Must be a positive integer of length 1.

shape1, shape2

the two (positive) shape parameters of the standard beta distribution. They are called a and b in beta respectively.

log, log.p

Logical. If TRUE then all probabilities p are given as log(p).

Value

• dbetageom gives the density, pbetageom gives the distribution function, and rbetageom generates random deviates.

Details

The beta-geometric distribution is a geometric distribution whose probability of success is not a constant but it is generated from a beta distribution with parameters shape1 and shape2. Note that the mean of this beta distribution is shape1/(shape1+shape2), which therefore is the mean of the probability of success.

See Also

geometric, betaff, Beta.

Examples

shape1 = 1; shape2 = 2; y = 0:30
proby = dbetageom(y, shape1, shape2, log=FALSE)
plot(y, proby, type="h", col="blue", ylab="P[Y=y]", main=paste(
     "Y ~ Beta-geometric(shape1=",shape1,", shape2=",shape2,")", sep=""))
sum(proby)