dist_bernoulli
The Bernoulli distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_bernoulli(prob)
Arguments
prob |
The probability of success on each trial, |
Details
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.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
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
Examples
dist <- dist_bernoulli(prob = c(0.05, 0.5, 0.3, 0.9, 0.1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7)