Chisquare
The Chi-square Distribution

Description

Calculates density, cumulative probability, quantile, and generate random sample for the chi-square distribution (continuous).

Usage

dchisq(x, df, ncp = 0, log = FALSE) # density
pchisq(q, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) # probability
qchisq(p, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) # quantile
rchisq(n, df, ncp = 0) # random

Arguments

x, q numeric vectors in the range [0, Inf) that specify the quantiles.
p a numeric vector in the range [0, 1] that specifies the probabilities.
n an integer scalar in the range [0, Inf) that specifies the number of random samples requested. If the input value is not an integer, it is truncated. If length(n) is greater than 1, the random function returns length(n) random samples.
df a numeric vector in the range [0, Inf) that specifies the degree of freedom.
ncp a numeric vector in the range [0, Inf) that specifies the noncentrality parameter.
log a logical value. If FALSE (default), the density function returns the density itself. If TRUE, it returns the log of the density.
lower.tail a logical value. If TRUE (default), the probability supplied to the quantile function or returned by the probability function is P[X <= x]. If FALSE, it is P[X > x].
log.p a logical value. If FALSE (default), the probability supplied to the quantile function or returned by the probability function is the probability itself. If TRUE, it is the log of the probability.

Details

The distribution parameter(s) are replicated cyclically to be the same length as the input x, q, p, or the number of random samples requested.
Missing values (NAs) in the input or the distribution parameter(s) will cause the corresponding elements of the result to be missing.
Value
returns density (dchisq), cumulative probability (pchisq), quantile (qchisq), or random sample (rchisq) for the chi-square distribution with parameter df and an optional noncentrality parameter ncp.
Side Effects
If the .Random.seed dataset exists, the random sample function updates its value. The random sample function creates the .Random.seed dataset if it does not exist.
Background
The chi-square distribution is a family of continuous probability distributions defined on the interval [0, Inf) and parameterized by a positive parameter df.
References
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vol. 2. Houghton-Mifflin, Boston.
Posten, H. O. (1989). An effective algorithm for the noncentral chi-squared distribution function. The American Statistician 43 261-263.
See Also
set.seed, Gamma, Normal, FALSE
Examples
# two ways to calculate p-value for stat 
stat <- 20; df <- 8
1 - pchisq(stat, df) 
pchisq(stat, df, lower.tail = FALSE)

# power of a test for several noncentrality values 
1 - pchisq(qchisq(.95, 8), 8, 0:10)
Package stats version 6.1.1-7
Package Index