Name  RNG  CDF  

Beta Distribution  rbeta 
dbeta 
pbeta

Binomial Distribution  rbinom 
dbinom 
pbinom

Cauchy Distribution  rcauchy 
dcauchy 
pcauchy

$\chi^2$ Distribution  rchisq 
dchisq 
pchisq

Exponential Distribution  rexp 
dexp 
pexp

F Distribution  rf 
df 
pf

Gamma Distribution  rgamma 
dgamma 
pgamma

Geometric Distribution  rgeom 
dgeom 
pgeom

Hypergeometric Distribution  rhyper 
dhyper 
phyper

Logistic Distribution  rlogis 
dlogis 
plogis

Log Normal Distribution  rlnorm 
dlnorm 
plnorm

Negative Binomial Distribution  rnbinom 
dnbinom 
pnbinom

Normal Distribution  rnorm 
dnorm 
pnorm

Poisson Distribution  rpois 
dpois 
ppois

$t$ Distribution  rt 
dt 
pt

Uniform Distribution  runif 
dunif 
punif

Weibull Distribution  rweibull 
dweibull 
pweibull

name
: Random Number GeneratorExample 1
heights = rnorm(10, mean=188, sd=3) > 186.0 191.2 187.6 187.9 186.6 187.2 187.2 189.5 190.8 186.4
Example 2
coinFlips = rbinom(10, size=10, prob=0.5) > 3 4 6 5 7 6 5 8 5 6
name
: Probability Density FunctionCalculates the density of some probability distribution
x = seq(from=5, to=5, length=10) normalDensity = dnorm(x, mean=0, sd=1) round(normalDensity, 2) [1] 0.00 0.00 0.01 0.10 0.34 0.34 0.10 0.01 0.00 0.00
Same with 15 :
x = seq(from=3, to=3, length=15) normalDensity = dnorm(x, mean=0, sd=1) r = round(normalDensity, 2) bp = barplot(r) xspline(x=bp, y=r, lwd=2, shape=1, border="blue") text(x=bp, y=r+0.03, labels=as.character(r), xpd=TRUE, cex=0.7)
So we can see that it generates the values of the density function
Same for the Binomial distribution:
x = seq(0, 10, by=1) binomialDensity = dbinom(x, size=10, prob=0.5) round(binomialDensity,2)
name
: Cumulative Distribution FunctionWhen you need to know what is the probability of $X \geqslant x$ for some $x$.
For example, you're doing an $F$Test
1  pf(3.446, df1=1, df2=85)
Function sample
draws a random sample
function(x, size, replace=FALSE, prob=NULL)
replace=T
for sampling with replacements = seq(0, 20) > 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 sample(s, size=10) > 8 4 11 12 20 7 19 18 1 14 sample(s, size=10, replace=T) > 6 17 18 7 2 9 18 0 7 5
Note that 7 and 18 are selected twice for the sample with replacement
The sample can be draw with specified probability
dnorm(seq(3, 3, length=length(s))) sample(s, size=10, replace=T, prob=n) > 9 7 11 11 1 13 11 14 5 6
It is very useful for Bootstrapping
reps = 1000 n = length(data) sampl = sample(data, size=n) bs = replicate(reps, mean(sample(sampl, size=n, replace=T)))
When we experiment, we typically want to reproduce it later
set.seed(12345)