dist_geometric
The Geometric Distribution
Description
The Geometric distribution can be thought of as a generalization
of the dist_bernoulli() distribution where we ask: "if I keep flipping a
coin with probability p of heads, what is the probability I need
k flips before I get my first heads?" The Geometric
distribution is a special case of Negative Binomial distribution.
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_geometric(prob)
Arguments
prob |
probability of success in each trial. |
Details
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a Geometric random variable with
success probability p = p. Note that there are multiple
parameterizations of the Geometric distribution.
Support: 0 < p < 1, x = 0, 1, …
Mean: \frac{1-p}{p}
Variance: \frac{1-p}{p^2}
Probability mass function (p.m.f):
P(X = x) = p(1-p)^x,
Cumulative distribution function (c.d.f):
P(X ≤ x) = 1 - (1-p)^{x+1}
Moment generating function (m.g.f):
E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t}
See Also
Examples
dist <- dist_geometric(prob = c(0.2, 0.5, 0.8)) 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)