R语言卡方(chisq)分布

若n个相互独立的随机变量ξ₁，ξ₂，...,ξn ，均服从标准正态分布（也称独立同分布于标准正态分布），则这n个服从标准正态分布的随机变量的平方和构成一新的随机变量，其分布规律称为卡方分布（chi-square distribution）。

 

The (non-central) Chi-Squared Distribution

Description

Density, distribution function, quantile function and random generation for the chi-squared (chi^2) distribution with df degrees of freedom and optional non-centrality parameter ncp.

Usage

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

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).
ncp	non-centrality parameter (non-negative).
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].

####卡方(chisq)分布
# 1.卡方分布中抽样函数rchisq
n = 100
df <- 10
rchisq(n, df, ncp = 0)

# 2.卡方分布概率密度函数
x <- seq(0,30,0.1) # x为非负整数，表达次数。
y <- dchisq(x,df)
plot(x,y)

# 3.卡方分布累积概率
x <- seq(1,20,0.1)
plot(x,dchisq(x,df=10))
# P[X ≤ x]
pchisq(5, df=10)
# P[X > x]
pchisq(5, df=10,lower.tail = FALSE)

# probabilities p are given as log(p).
pchisq(5, df=10,log.p = TRUE)

# 4.qchisq函数(pchisq的反函数)
# 累积概率为0.95时的x值
qchisq(0.95, df=1)
qchisq(0.95, df=10)
qchisq(0.95, df=100)