Betageom {VGAM} | R Documentation

## 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. 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)`.

### 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.

### Value

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

### Note

`pbetageom` can be particularly slow.

### Author(s)

T. W. Yee

### See Also

`geometric`, `betaff`, `Beta`.

### Examples

    ## Not run:
    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)

    ## End(Not run)

[Package VGAM version 1.0-3 Index]