# expgeometricUC: The Exponential Geometric Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, distribution function, quantile function and random generation for the exponential geometric distribution.

## Usage

 ```1 2 3 4``` ```dexpgeom(x, scale = 1, shape, log = FALSE) pexpgeom(q, scale = 1, shape) qexpgeom(p, scale = 1, shape) rexpgeom(n, scale = 1, shape) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. If `length(n) > 1` then the length is taken to be the number required. `scale, shape` positive scale and shape parameters. `log` Logical. If `log = TRUE` then the logarithm of the density is returned.

## Details

See `expgeometric`, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

## Value

`dexpgeom` gives the density, `pexpgeom` gives the distribution function, `qexpgeom` gives the quantile function, and `rexpgeom` generates random deviates.

## Note

We define `scale` as the reciprocal of the scale parameter used by Adamidis and Loukas (1998).

## Author(s)

J. G. Lauder and T. W. Yee

`expgeometric`, `exponential`, `geometric`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## Not run: shape <- 0.5; scale <- 1; nn <- 501 x <- seq(-0.10, 3.0, len = nn) plot(x, dexpgeom(x, scale, shape), type = "l", las = 1, ylim = c(0, 2), ylab = paste("[dp]expgeom(shape = ", shape, ", scale = ", scale, ")"), col = "blue", cex.main = 0.8, main = "Blue is density, red is cumulative distribution function", sub = "Purple lines are the 10,20,...,90 percentiles") lines(x, pexpgeom(x, scale, shape), col = "red") probs <- seq(0.1, 0.9, by = 0.1) Q <- qexpgeom(probs, scale, shape) lines(Q, dexpgeom(Q, scale, shape), col = "purple", lty = 3, type = "h") lines(Q, pexpgeom(Q, scale, shape), col = "purple", lty = 3, type = "h") abline(h = probs, col = "purple", lty = 3) max(abs(pexpgeom(Q, scale, shape) - probs)) # Should be 0 ## End(Not run) ```

### Example output ```Loading required package: stats4