## The Chi Distribution

### Description

Density, distribution function, quantile function and random generation for the chi distribution with `df` degrees of freedom.

### Usage

```dchi(x, df = 2)
pchi(q, df = 2, lower.tail = TRUE, ...)
qchi(p, df = 2, lower.tail = TRUE)
rchi(n, df = 2)
```

### Arguments

 `x,q` vector of quantiles. `p` vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required. `df` degrees of freedom (non-negative, but can be non-integer). `lower.tail` logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. `...` additional arguments to be passed to the function `integrate`.

### Details

The chi distribution with `df` = n > 0 degrees of freedom has density

f_n (x) = 2^(1-n/2) x^(n-1) e^(-(x^2)/2) / Gamma(n/2)

for x > 0. This distribution is used to describe the square root of a variable distributed according to a chi-square distribution.

### Value

`dchi` gives the density, `pchi` gives the distribution function, `qchi` gives the quantile function, and `rchi` generates random deviates.

### Author(s)

Clement Calenge clement.calenge@ofb.gouv.fr

### References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, 3rd ed. Wiley, New York.

`Chisquare`

### Examples

```
opar <- par(mfrow = c(2,2))

hist(rchi(100), ncla = 20, main="The Chi distribution")

plot(tutu <- seq(0, 5, length=20), dchi(tutu, df = 2), xlab = "x",
ylab = "probability density", type = "l")

plot(tutu, pchi(tutu), xlab = "x", ylab = "Repartition function",
type = "l")

par(opar)

```