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R - Random Numbers Generator
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  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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