Bernoulli: Create a Bernoulli distribution

Description Usage Arguments Details Value See Also Examples

View source: R/Bernoulli.R

Description

Bernoulli distributions are used to represent events like coin flips when there is single trial that is either successful or unsuccessful. The Bernoulli distribution is a special case of the Binomial() distribution with n = 1.

Usage

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Bernoulli(p = 0.5)

Arguments

p

The success probability for the distribution. p can be any value in [0, 1], and defaults to 0.5.

Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions3, where the math will render with additional detail.

In the following, let X be a Bernoulli random variable with parameter p = p. Some textbooks also define q = 1 - p, or use π instead of p.

The Bernoulli probability distribution is widely used to model binary variables, such as 'failure' and 'success'. The most typical example is the flip of a coin, when p is thought as the probability of flipping a head, and q = 1 - p is the probability of flipping a tail.

Support: {0, 1}

Mean: p

Variance: p (1 - p)

Probability mass function (p.m.f):

P(X = x) = p^x (1 - p)^(1-x)

Cumulative distribution function (c.d.f):

P(X ≤ x) = (1 - p) 1_{[0, 1)}(x) + 1_{1}(x)

Moment generating function (m.g.f):

E(e^(tX)) = (1 - p) + p e^t

Value

A Bernoulli object.

See Also

Other discrete distributions: Binomial(), Categorical(), Geometric(), HyperGeometric(), Multinomial(), NegativeBinomial(), Poisson()

Examples

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set.seed(27)

X <- Bernoulli(0.7)
X

mean(X)
variance(X)
skewness(X)
kurtosis(X)

random(X, 10)
pdf(X, 1)
log_pdf(X, 1)
cdf(X, 0)
quantile(X, 0.7)

cdf(X, quantile(X, 0.7))
quantile(X, cdf(X, 0.7))

alexpghayes/distributions documentation built on April 8, 2021, 5:55 a.m.