betageomUC: The Beta-Geometric Distribution In VGAM: Vector Generalized Linear and Additive Models

Description

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

Usage

 ```1 2 3``` ```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

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

Examples

 ```1 2 3 4 5 6 7 8``` ```## 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) ```

Example output

```Loading required package: stats4