# geometric: Create a Geometric distribution In alexpghayes/distributions: Probability Distributions as S3 Objects

## Description

The Geometric distribution can be thought of as a generalization of the 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.

## Usage

 1 Geometric(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 and much greater clarity.

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}

## Value

A Geometric object.

Other discrete distributions: Bernoulli(), Binomial(), Categorical(), HyperGeometric(), Multinomial(), NegativeBinomial(), Poisson()
  1 2 3 4 5 6 7 8 9 10 11 12 set.seed(27) X <- Geometric(0.3) X random(X, 10) pdf(X, 2) log_pdf(X, 2) cdf(X, 4) quantile(X, 0.7)