# gumbelIIUC: The Gumbel-II Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, cumulative distribution function, quantile function and random generation for the Gumbel-II distribution.

## Usage

 ```1 2 3 4``` ```dgumbelII(x, scale = 1, shape, log = FALSE) pgumbelII(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) qgumbelII(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) rgumbelII(n, scale = 1, shape) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Same as in `runif`. `log` Logical. If `log = TRUE` then the logarithm of the density is returned. `lower.tail, log.p` Same meaning as in `pnorm` or `qnorm`. `shape, scale` positive shape and scale parameters.

## Details

See `gumbelII` for details.

## Value

`dgumbelII` gives the density, `pgumbelII` gives the cumulative distribution function, `qgumbelII` gives the quantile function, and `rgumbelII` generates random deviates.

## Author(s)

T. W. Yee and Kai Huang

`gumbelII`, `dgumbel`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```probs <- seq(0.01, 0.99, by = 0.01) Scale <- exp(1); Shape <- exp( 0.5); max(abs(pgumbelII(qgumbelII(p = probs, shape = Shape, Scale), shape = Shape, Scale) - probs)) # Should be 0 ## Not run: x <- seq(-0.1, 10, by = 0.01); plot(x, dgumbelII(x, shape = Shape, Scale), type = "l", col = "blue", las = 1, main = "Blue is density, orange is cumulative distribution function", sub = "Purple lines are the 10,20,...,90 percentiles", ylab = "", ylim = 0:1) abline(h = 0, col = "blue", lty = 2) lines(x, pgumbelII(x, shape = Shape, Scale), col = "orange") probs <- seq(0.1, 0.9, by = 0.1) Q <- qgumbelII(probs, shape = Shape, Scale) lines(Q, dgumbelII(Q, Scale, Shape), col = "purple", lty = 3, type = "h") pgumbelII(Q, shape = Shape, Scale) - probs # Should be all zero abline(h = probs, col = "purple", lty = 3) ## End(Not run) ```