Create a Bernoulli distribution
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.
Bernoulli(p = 0.5)
p |
The success probability for the distribution. |
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
A Bernoulli object.
Other discrete distributions: Binomial,
Categorical, Geometric,
HyperGeometric, Multinomial,
NegativeBinomial, Poisson
set.seed(27) X <- Bernoulli(0.7) 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))
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