The Chi Distribution

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Description

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

Usage

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

Author(s)

Clement Calenge clement.calenge@oncfs.gouv.fr

References

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

See Also

Chisquare

Examples

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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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