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. 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)`.

### 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 0.7-9 Index]