# Distributions in R ¶

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This is a summary of the functions used to generate distributions in R. The functions are starting with r/p/q/d followed by the name of the distribution in R.

The values for [dist] will be given in the next section.

• r[dist]: generate a distribution
• p[dist]: $P(X \le k)$
• q[dist]: quantile function (Inverse cumulative distribution function)
• d[dist]: density function or mass function ($P(X=k)$)

## Well-known distributions ¶

The values for [dist] that we will use a lot are

• Bernoulli ($B(p0.5)$): rbinom(n=10,size=1,prob=0.5) (size is always 1 otherwise it's a binomial distribution)
• Binomial ($B(n=5,p=0.5)$): rbinom(n=10,size=5,prob=0.5)
• Cauchy: rcauchy(n=10,location=0,scale=1)
• chi-square (Khi-deux): rchisq(n = 10, df = 2)
• exponential: rexp(n=10, rate = 1)
• Gamma: rgamma(n = 10, shape = 5, rate = 1)
• Geometric $G(p)$: rgeom(n = 10, prob = 0.7)
• HyperGeometric: rhyper(nn = 10, m = 10, n = 5, k = 10)
• Normal: rnorm(n = 10, mean = 0, sigma = 1)
• Poisson: rpois(n = 10, lambda = 0.05)
• Weibull: rweibull(n = 10, shape = 2, scale = 2)

## Notes ¶

NOTE: specifying the names of the parameters IS NOT MANDATORY like rbinom(10, 1, 0.5) is working. This is up to you.

NOTE (2): The call rbinom(n=10,size=1,prob=0.5) could be described as

• generating a vector of size $n=10$
• in which, each value is the result of a Bernoulli distribution $B(0.5)$

For instance, the call above would give

# not random, we pick a seed
# so anyone running the code will have the same sample
set.seed(0)
# generating
s <- rbinom(n=10,size=1,prob=0.5)
s # <=> print(s)
#  1 0 0 1 1 0 1 1 1 1


In the resulting vector, we can read that in the first experience, we got one success. In the second, we had a failure, etc. Bernoulli's distribution is like flipping a coin if p=0.5, and if $p \neq 0.5$ then the coin is a rigged coin.