VGAM (version 1.1-6)

# 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. 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.

## 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.

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

## Examples

Run this code
``````# 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)
# }
``````

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