# Random Numbers Generator

# Random permutations

To generate random permutation of 5 numbers:

sample(5)
# [1] 4 5 3 1 2

To generate random permutation of any vector:

sample(10:15)
# [1] 11 15 12 10 14 13

One could also use the package pracma

randperm(a, k)
# Generates one random permutation of k of the elements a, if a is a vector,
# or of 1:a if a is a single integer.
# a: integer or numeric vector of some length n.
# k: integer, smaller as a or length(a).

# Examples
library(pracma)
randperm(1:10, 3)
[1] 3 7 9

randperm(10, 10)
[1]  4  5 10  8  2  7  6  9  3  1

randperm(seq(2, 10, by=2))
[1]  6  4 10  2  8

# Random number generator's reproducibility

When expecting someone to reproduce an R code that has random elements in it, the set.seed() function becomes very handy. For example, these two lines will always produce different output (because that is the whole point of random number generators):

> sample(1:10,5)
[1]  6  9  2  7 10
> sample(1:10,5)
[1]  7  6  1  2 10

These two will also produce different outputs:

> rnorm(5)
[1]  0.4874291  0.7383247  0.5757814 -0.3053884  1.5117812
> rnorm(5)
[1]  0.38984324 -0.62124058 -2.21469989  1.12493092 -0.04493361

However, if we set the seed to something identical in both cases (most people use 1 for simplicity), we get two identical samples:

> set.seed(1)
> sample(letters,2)
[1] "g" "j"
> set.seed(1)
> sample(letters,2)
[1] "g" "j"

and same with, say, rexp() draws:

> set.seed(1)
> rexp(5)
[1] 0.7551818 1.1816428 0.1457067 0.1397953 0.4360686
> set.seed(1)
> rexp(5)
[1] 0.7551818 1.1816428 0.1457067 0.1397953 0.4360686

# Generating random numbers using various density functions

Below are examples of generating 5 random numbers using various probability distributions.

# Uniform distribution between 0 and 10

runif(5, min=0, max=10)
[1] 2.1724399 8.9209930 6.1969249 9.3303321 2.4054102

# Normal distribution with 0 mean and standard deviation of 1

rnorm(5, mean=0, sd=1)
[1] -0.97414402 -0.85722281 -0.08555494 -0.37444299  1.20032409

# Binomial distribution with 10 trials and success probability of 0.5

rbinom(5, size=10, prob=0.5)
[1] 4 3 5 2 3

# Geometric distribution with 0.2 success probability

rgeom(5, prob=0.2)
[1] 14  8 11  1  3

# Hypergeometric distribution with 3 white balls, 10 black balls and 5 draws

rhyper(5, m=3, n=10, k=5)
[1] 2 0 1 1 1

# Negative Binomial distribution with 10 trials and success probability of 0.8

rnbinom(5, size=10, prob=0.8)
[1] 3 1 3 4 2

# Poisson distribution with mean and variance (lambda) of 2

rpois(5, lambda=2)
[1] 2 1 2 3 4

# Exponential distribution with the rate of 1.5

rexp(5, rate=1.5)
[1] 1.8993303 0.4799358 0.5578280 1.5630711 0.6228000

# Logistic distribution with 0 location and scale of 1

rlogis(5, location=0, scale=1)
[1]  0.9498992 -1.0287433 -0.4192311  0.7028510 -1.2095458

# Chi-squared distribution with 15 degrees of freedom

rchisq(5, df=15)
[1] 14.89209 19.36947 10.27745 19.48376 23.32898

# Beta distribution with shape parameters a=1 and b=0.5

rbeta(5, shape1=1, shape2=0.5)
[1] 0.1670306 0.5321586 0.9869520 0.9548993 0.9999737

# Gamma distribution with shape parameter of 3 and scale=0.5

rgamma(5, shape=3, scale=0.5)
[1] 2.2445984 0.7934152 3.2366673 2.2897537 0.8573059

# Cauchy distribution with 0 location and scale of 1

rcauchy(5, location=0, scale=1)
[1] -0.01285116 -0.38918446  8.71016696 10.60293284 -0.68017185

# Log-normal distribution with 0 mean and standard deviation of 1 (on log scale)

rlnorm(5, meanlog=0, sdlog=1)
[1] 0.8725009 2.9433779 0.3329107 2.5976206 2.8171894

# Weibull distribution with shape parameter of 0.5 and scale of 1

rweibull(5, shape=0.5, scale=1)
[1] 0.337599112 1.307774557 7.233985075 5.840429942 0.005751181

# Wilcoxon distribution with 10 observations in the first sample and 20 in second.

rwilcox(5, 10, 20)
[1] 111  88  93 100 124

# Multinomial distribution with 5 object and 3 boxes using the specified probabilities

rmultinom(5, size=5, prob=c(0.1,0.1,0.8))
     [,1] [,2] [,3] [,4] [,5]
[1,]    0    0    1    1    0
[2,]    2    0    1    1    0
[3,]    3    5    3    3    5

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