# genrayleighUC: The Generalized Rayleigh Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, distribution function, quantile function and random generation for the generalized Rayleigh distribution.

## Usage

 ```1 2 3 4``` ```dgenray(x, scale = 1, shape, log = FALSE) pgenray(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) qgenray(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) rgenray(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. `lower.tail, log.p` Same meaning as in `pnorm` or `qnorm`.

## Details

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

## Value

`dgenray` gives the density, `pgenray` gives the distribution function, `qgenray` gives the quantile function, and `rgenray` generates random deviates.

## Note

We define `scale` as the reciprocal of the scale parameter used by Kundu and Raqab (2005).

## Author(s)

Kai Huang and J. G. Lauder and T. W. Yee

`genrayleigh`, `rayleigh`.
 ``` 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, dgenray(x, shape, scale = Scale), type = "l", las = 1, ylim = c(0, 1.2), ylab = paste("[dp]genray(shape = ", shape, ", scale = ", Scale, ")"), col = "blue", cex.main = 0.8, main = "Blue is density, orange is cumulative distribution function", sub = "Purple lines are the 10,20,...,90 percentiles") lines(x, pgenray(x, shape, scale = Scale), col = "orange") probs <- seq(0.1, 0.9, by = 0.1) Q <- qgenray(probs, shape, scale = Scale) lines(Q, dgenray(Q, shape, scale = Scale), col = "purple", lty = 3, type = "h") lines(Q, pgenray(Q, shape, scale = Scale), col = "purple", lty = 3, type = "h") abline(h = probs, col = "purple", lty = 3) max(abs(pgenray(Q, shape, scale = Scale) - probs)) # Should be 0 ## End(Not run) ```