Chi: 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.

vector of probabilities.

number of observations. If length(n) > 1, the length is taken to be the number required.

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.

Value

dchi gives the density, pchisq gives the distribution function, qchisq gives the quantile function, and rchisq generates random deviates.

Details

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

$$f_n (x) = 2^{1-n/2} x^{n-1} e^{\frac{-(x^2)}{2}} / \Gamma (n/2)$$

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

References

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

Examples

Run this code

# NOT RUN {
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)

# }

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