ML Wiki

Simulation in R

Distributions

Name	RNG	PDF	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

rname: Random Number Generator

Example 1

• Generate 10 random values from Normal Distribution
• with standard deviation 3 and mean 188

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

• Generates 10 random values from Binomial Distribution
• flipping a coin 10 times = 10 independent experiments with probability 0.5

coinFlips = rbinom(10, size=10, prob=0.5)
> 3 4 6 5 7 6 5 8 5 6

dname: Probability Density Function

Calculates 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)

Code [1] [2]

So we can see that it generates the values of the density function

• 
• may be useful for Statistical Tests of Significance

Same for the Binomial distribution:

x = seq(0, 10, by=1)
binomialDensity = dbinom(x, size=10, prob=0.5)
round(binomialDensity,2)

pname: Cumulative Distribution Function

When you need to know what is the probability of $X \geqslant x$ for some $x$.

For example, you're doing an $F$-Test

• you obtained $F = 3.446$
• $F$ statistic follows the $F$ Distribution: $F \sim F(\text{df1}, \text{df2})$
• so you can calculate the $p$-value:

1 - pf(3.446, df1=1, df2=85)

Sampling

Function sample draws a random sample

• function(x, size, replace=FALSE, prob=NULL)
• replace=T for sampling with replacement

s = 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

• e.g. suppose we want to sample with normal distribution

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 

• note that 11 gets selected 3 times,
• because the probability of selecting it is quite high: 0.3989

Bootstrapping

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)))

Reproducibility

When we experiment, we typically want to reproduce it later

• so it's important to generate the same "random" data
• for that we can set the seed for PRG
• set.seed(12345)

Source

• Data Analysis (coursera)