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.

dist_geometric(prob)

## Arguments

prob probability of success in each trial. 0 < prob <= 1.

## 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, $$x = 0, 1, \dots$$

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):

$$P(X \le x) = 1 - (1-p)^{x+1}$$

Moment generating function (m.g.f):

$$E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t}$$

## Examples

dist <- dist_geometric(prob = c(0.2, 0.5, 0.8))

dist
#> <distribution[3]>
#> [1] Geometric(0.2) Geometric(0.5) Geometric(0.8)mean(dist)
#> [1] 4.00 1.00 0.25variance(dist)
#> [1] 20.0000  2.0000  0.3125skewness(dist)
#> [1] 2.012461 2.121320 2.683282kurtosis(dist)
#> [1] 6.05 6.50 9.20
generate(dist, 10)
#> [[1]]
#>  [1] 0 3 7 2 2 2 8 2 4 3
#>
#> [[2]]
#>  [1] 0 0 0 2 0 0 5 0 0 0
#>
#> [[3]]
#>  [1] 0 0 1 0 0 0 0 0 1 0
#>
density(dist, 2)
#> [1] 0.128 0.125 0.032density(dist, 2, log = TRUE)
#> [1] -2.055725 -2.079442 -3.442019
cdf(dist, 4)
#> [1] 0.67232 0.96875 0.99968
quantile(dist, 0.7)
#> [1] 5 1 0