# slashUC: Slash Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density function, distribution function, and random generation for the slash distribution.

## Usage

 ```1 2 3 4``` ```dslash(x, mu = 0, sigma = 1, log = FALSE, smallno = .Machine\$double.eps*1000) pslash(q, mu = 0, sigma = 1, very.negative = -10000, lower.tail = TRUE, log.p = FALSE) rslash(n, mu = 0, sigma = 1) ```

## Arguments

 `x, q` vector of quantiles. `n` Same as `runif`. `mu, sigma` the mean and standard deviation of the univariate normal distribution. `log` Logical. If `TRUE` then the logarithm of the density is returned. `very.negative` Numeric, of length 1. A large negative value. For `(q-mu)/sigma` values less than this, the value 0 is returned because `integrate` tends to fail. A warning is issued. Similarly, if `(q-mu)/sigma` is greater than `abs(very.negative)` then 1 is returned with a warning. `smallno` See `slash`. `lower.tail, log.p` Same meaning as in `pnorm` or `qnorm`.

## Details

See `slash`, the VGAM family function for estimating the two parameters by maximum likelihood estimation, for the formula of the probability density function and other details.

Function `pslash` uses a `for ()` loop and `integrate`, meaning it's very slow. It may also be inaccurate for extreme values of `q`, and returns with 1 or 0 values when too extreme compared to `very.negative`.

## Value

`dslash` gives the density, and `pslash` gives the distribution function, `rslash` generates random deviates.

## Note

`pslash` is very slow.

## Author(s)

Thomas W. Yee and C. S. Chee

`slash`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## Not run: curve(dslash, col = "blue", ylab = "f(x)", -5, 5, ylim = c(0, 0.4), las = 1, main = "Standard slash, normal and Cauchy densities", lwd = 2) curve(dnorm, col = "black", lty = 2, lwd = 2, add = TRUE) curve(dcauchy, col = "orange", lty = 3, lwd = 2, add = TRUE) legend("topleft", c("slash", "normal", "Cauchy"), lty = 1:3, col = c("blue","black","orange"), lwd = 2) curve(pslash, col = "blue", -5, 5, ylim = 0:1) pslash(c(-Inf, -20000, 20000, Inf)) # Gives a warning ## End(Not run) ```