# dist-std: Student-t Distribution In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

## Description

Functions to compute density, distribution function, quantile function and to generate random variates for the Student-t distribution.

## Usage

 ```1 2 3 4``` ```dstd(x, mean = 0, sd = 1, nu = 5, log = FALSE) pstd(q, mean = 0, sd = 1, nu = 5) qstd(p, mean = 0, sd = 1, nu = 5) rstd(n, mean = 0, sd = 1, nu = 5) ```

## Arguments

 `mean, sd, nu` location parameter `mean`, scale parameter `sd`, shape parameter `nu`. `n` the number of observations. `p` a numeric vector of probabilities. `x, q` a numeric vector of quantiles. `log` a logical; if TRUE, densities are given as log densities.

## Value

`d*` returns the density, `p*` returns the distribution function, `q*` returns the quantile function, and `r*` generates random deviates,
all values are numeric vectors.

## Author(s)

Diethelm Wuertz for the Rmetrics R-port.

## References

Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## std - par(mfrow = c(2, 2)) set.seed(1953) r = rstd(n = 1000) plot(r, type = "l", main = "sstd", col = "steelblue") # Plot empirical density and compare with true density: hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue") box() x = seq(min(r), max(r), length = 201) lines(x, dstd(x), lwd = 2) # Plot df and compare with true df: plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue", ylab = "Probability") lines(x, pstd(x), lwd = 2) # Compute quantiles: round(qstd(pstd(q = seq(-1, 5, by = 1))), digits = 6) ```

### Example output

```Loading required package: timeDate

Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
[1] -1  0  1  2  3  4  5
```

fGarch documentation built on Nov. 17, 2017, 2:15 p.m.