The Beta-Geometric Distribution

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

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. Same as runif.

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.

Author

T. W. Yee

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.

Note

pbetageom can be particularly slow.

See also

geometric, betaff, Beta.

Examples

if (FALSE) { # \dontrun{
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 = paste0(
     "Y ~ Beta-geometric(shape1=", shape1,", shape2=", shape2, ")"))
sum(proby)
} # }