原文地址：[整理] 利用R生成随机分布的方法
作者：周庭锐教授
[整理] 利用R生成随机分布的方法
文/周庭锐
夜里复习各种统计分布的模拟、拟合、验证的R编程，顺手整理一下。
（不懂怎么一回事，刚刚贴上了，然后一转眼就消失了。新浪博客里闹鬼？）
d: density
p: distribution function
q: quantile function
r: random deviates
rexp The Exponential Distribution
dexp(x, rate = 1, log = FALSE)
pexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)
qexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE)
rexp(n, rate = 1)
rf The F Distribution
df(x, df1, df2, ncp, log = FALSE)
pf(q, df1, df2, ncp, lower.tail = TRUE, log.p = FALSE)
qf(p, df1, df2, ncp, lower.tail = TRUE, log.p = FALSE)
rf(n, df1, df2, ncp)
rgamma The Gamma Distribution
dgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rgamma(n, shape, rate = 1, scale = 1/rate)
rgeom The Geometric Distribution
dgeom(x, prob, log = FALSE)
pgeom(q, prob, lower.tail = TRUE, log.p = FALSE)
qgeom(p, prob, lower.tail = TRUE, log.p = FALSE)
rgeom(n, prob)
rhyper The Hypergeometric Distribution
dhyper(x, m, n, k, log = FALSE)
phyper(q, m, n, k, lower.tail = TRUE, log.p = FALSE)
qhyper(p, m, n, k, lower.tail = TRUE, log.p = FALSE)
rhyper(nn, m, n, k)
rlnorm The Log Normal Distribution
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)
plnorm(q, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)
qlnorm(p, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)
rlnorm(n, meanlog = 0, sdlog = 1)
rlogis The Logistic Distribution
dlogis(x, location = 0, scale = 1, log = FALSE)
plogis(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qlogis(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rlogis(n, location = 0, scale = 1)
rmultinom The Multinomial Distribution
rmultinom(n, size, prob)
dmultinom(x, size = NULL, prob, log = FALSE)
rnbinom The Negative Binomial Distribution
dnbinom(x, size, prob, mu, log = FALSE)
pnbinom(q, size, prob, mu, lower.tail = TRUE, log.p = FALSE)
qnbinom(p, size, prob, mu, lower.tail = TRUE, log.p = FALSE)
rnbinom(n, size, prob, mu)
rnorm The Normal Distribution
dnorm(x, mean = 0, sd = 1, log = FALSE)
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
rnorm(n, mean = 0, sd = 1)
rpois The Poisson Distribution
dpois(x, lambda, log = FALSE)
ppois(q, lambda, lower.tail = TRUE, log.p = FALSE)
qpois(p, lambda, lower.tail = TRUE, log.p = FALSE)
rpois(n, lambda)
rsignrank Distribution of the Wilcoxon Signed Rank Statistic
dsignrank(x, n, log = FALSE)
psignrank(q, n, lower.tail = TRUE, log.p = FALSE)
qsignrank(p, n, lower.tail = TRUE, log.p = FALSE)
rsignrank(nn, n)
rt The Student t Distribution
dt(x, df, ncp, log = FALSE)
pt(q, df, ncp, lower.tail = TRUE, log.p = FALSE)
qt(p, df, ncp, lower.tail = TRUE, log.p = FALSE)
rt(n, df, ncp)
runif The Uniform Distribution
dunif(x, min=0, max=1, log = FALSE)
punif(q, min=0, max=1, lower.tail = TRUE, log.p = FALSE)
qunif(p, min=0, max=1, lower.tail = TRUE, log.p = FALSE)
runif(n, min=0, max=1)
rweibull The Weibull Distribution
dweibull(x, shape, scale = 1, log = FALSE)
pweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
qweibull(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
rweibull(n, shape, scale = 1)
rwilcox Distribution of the Wilcoxon Rank Sum Statistic
dwilcox(x, m, n, log = FALSE)
pwilcox(q, m, n, lower.tail = TRUE, log.p = FALSE)
qwilcox(p, m, n, lower.tail = TRUE, log.p = FALSE)
rwilcox(nn, m, n)
sample The Discrete Uniform Distribution
sample(x, size, replace = FALSE, prob = NULL)
sample.int(n, size = n, replace = FALSE, prob = NULL)
拟合：
连续型变量：
大样本：Kolmogorov-Smirnov检验
ks.test(x, y, ...,
alternative = c("two.sided", "less", "greater"),
exact = NULL)
小样本：Shapiro-Wilk检验
shapiro.test(x)
离散型变量：方差齐次性检验
fligner.test(x, ...)
## Default S3 method:
fligner.test(x, g, ...)
## S3 method for class 'formula'
fligner.test(formula, data, subset, na.action, ...)
或
mood.test(x, ...)
## Default S3 method:
mood.test(x, y,
alternative = c("two.sided", "less", "greater"), ...)
## S3 method for class 'formula'
mood.test(formula, data, subset, na.action, ...)
