R语言柯西(cauchy)分布

 柯西分布是一个数学期望不存在的连续型概率分布。当随机变量X满足它的概率密度函数时，称X服从柯西分布。

The Cauchy Distribution

Description

Density, distribution function, quantile function and random generation for the Cauchy distribution with location parameter location and scale parameter scale.

Usage

dcauchy(x, location = 0, scale = 1, log = FALSE)
pcauchy(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qcauchy(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rcauchy(n, location = 0, scale = 1)

Arguments

####柯西(cauchy)分布
# 1.柯西分布中抽样函数rcauchy
# location：x0; scale:gamma
n = 100
rate <- 1
rcauchy(n, location = 0, scale = 1)

# 2.柯西分布概率密度函数
x <- seq(0,10,0.1)
y <- dcauchy(x)
plot(x,y)

# 3.柯西分布累积概率
x <- seq(1,20,0.1)
plot(x,dcauchy(x,location = 0, scale = 2))
# P[X ≤ x]
pcauchy(1)
# P[X > x]
pcauchy(1,lower.tail = FALSE)

# probabilities p are given as log(p).
pcauchy(1,log.p = TRUE)

# 4.qcauchy函数(pcauchy的反函数)
# 累积概率为0.95时的x值
# x <- seq(-10,10,0.1)
# plot(x,pcauchy(x,location = 0, scale = 1))
qcauchy(0.95, location = 0, scale = 1)
qcauchy(0.995, location = 0, scale = 1)

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