gleam_stats/distributions/geometric
Functions related to discrete geometric random variables.
- Available Functions
Functions
pub fn geometric_cdf(x: Int, p: Float) -> Result(Float, String)
Evaluate, at a certain point $$x \in \mathbb{Z}$$, the cumulative distribution function (cdf) of a discrete geometric random variable with with parameter $$p \in (0, 1]$$ (the success probability).
The cdf is defined as:
\[ F(x; p) = \begin{cases} 1 - (1 - p)^{x + 1} &\text{if } x \geq 0, \\ 0 &\text{if } x < a \text{ or } x < 0. \end{cases} \]
Example:
import gleam_stats/distributions/geometric
import gleeunit/should
pub fn example() {
let p: Float = 0.5
// For illustrational purposes, evaluate the cdf at the
// point -100.0
geometric.geometric_cdf(-100.0, r, p)
|> should.equal(Ok(0.0))
}
pub fn geometric_mean(p: Float) -> Result(Float, String)
Analytically compute the mean of a discrete geometric random variable with parameter $$p \in (0, 1]$$ (the success probability).
The mean returned is: $$\frac{1 - p}{p}$$.
pub fn geometric_pmf(x: Int, p: Float) -> Result(Float, String)
Evaluate, at a certain point $$x \in \mathbb{Z}$$, the probability mass function (pmf) of a discrete geometric random variable with parameter $$p \in (0, 1]$$ (the success probability).
The pmf is defined as:
\[ f(x; p) = \begin{cases} (1 - p)^{x} \cdot p &\text{if } x \geq 0, \\ 0 &\text{if } x < 0. \end{cases} \]
Example:
import gleam_stats/distributions/geometric
import gleeunit/should
pub fn example() {
let p: Float = 0.5
// For illustrational purposes, evaluate the pmf at the
// point -100.0
geometric.geometric_pmf(-100.0, r, p)
|> should.equal(Ok(0.0))
}
pub fn geometric_random(stream: Iterator(Int), p: Float, m: Int) -> Result(
#(List(Int), Iterator(Int)),
String,
)
Generate $$m \in \mathbb{Z}_{>0}$$ random numbers from a discrete geometric distribution with parameter $$p \in (0, 1]$$ (the success probability).
The random numbers are generated using the inverse transform method.
Example:
import gleam/iterator.{Iterator}
import gleam_stats/generators
import gleam_stats/distributions/geometric
pub fn example() {
let seed: Int = 5
let seq: Int = 1
let p: Float = 0.5
assert Ok(out) =
generators.seed_pcg32(seed, seq)
|> geometric.geometric_random(r, p, 5_000)
let rands: List(Float) = pair.first(out)
let stream: Iterator(Int) = pair.second(out)
}
pub fn geometric_variance(p: Float) -> Result(Float, String)
Analytically compute the variance of a discrete geometric random variable with parameter $$p \in (0, 1]$$ (the success probability).
The variance returned is: $$\frac{1 - p}{p^{2}}$$.