gleam_stats - v1.1.0

gleam_stats/distributions/exponential

Functions related to continuous exponential random variables.

Functions

exponential_cdf

</> 
pub fn exponential_cdf(x: Float, lambda: Float) -> Result(
  Float,
  String,
)

Evaluate, at a certain point $$x \in (-\infty, +\infty)$$, the cumulative distribution function (cdf) of a continuous exponential random variable with given rate parameter $$\lambda \in (0, +\infty)$$.

The cdf is defined as:

\[ F(x; \lambda) = \begin{cases} 1 - e^{-\lambda \cdot x} &\text{if } x \geq 0, \\ 0 &\text{if } x < 0. \end{cases} \]

Example: 
 import gleam_stats/distributions/exponential
 import gleeunit/should

 pub fn example() {
   let lambda: Float = 1.
   // For illustrational purposes, evaluate the cdf at the 
   // point -100.0
   exponential.exponential_cdf(-100.0, lambda) 
   |> should.equal(Ok(0.0))
 }

exponential_mean

</> 
pub fn exponential_mean(lambda: Float) -> Result(Float, String)

Analytically compute the mean of a continuous exponential random variable
with given rate parameter $$\lambda \in (0, +\infty)$$.

The mean returned is: $$\frac{1}{\lambda}$$.

exponential_pdf

</> 
pub fn exponential_pdf(x: Float, lambda: Float) -> Result(
  Float,
  String,
)

Evaluate, at a certain point $$x \in (-\infty, +\infty)$$, the probability density function (pdf) of a continuous exponential random variable with given rate parameter $$\lambda \in (0, +\infty)$$.

The pdf is defined as:

\[ f(x; \lambda) = \begin{cases} \lambda \cdot e^{-\lambda \cdot x} &\text{if } x \geq 0, \\ 0 &\text{if } x < 0. \end{cases} \]

Example: 
 import gleam_stats/distributions/exponential
 import gleeunit/should

 pub fn example() {
   let lambda: Float = 1.
   // For illustrational purposes, evaluate the pdf at the 
   // point -100.0
   exponential.exponential_pdf(-100.0, lambda) 
   |> should.equal(Ok(0.0))
 }

exponential_random

</> 
pub fn exponential_random(stream: Iterator(Int), lambda: Float, m: Int) -> Result(
  #(List(Float), Iterator(Int)),
  String,
)

Generate $$m \in \mathbb{Z}_{>0}$$ random numbers from a continuous exponential distribution with given rate parameter $$\lambda \in (0, +\infty)$$.

The random numbers are generated using the inverse transform method.

Example: 
 import gleam/iterator.{Iterator}
 import gleam_stats/generators
 import gleam_stats/distributions/exponential

 pub fn example() {
   let seed: Int = 5
   let seq: Int = 1
   let lambda: Float = 1.
   assert Ok(out) =
     generators.seed_pcg32(seed, seq)
     |> exponential.exponential_random(lambda, 5_000)
   let rands: List(Float) = pair.first(out)
   let stream: Iterator(Int) = pair.second(out)
 }

exponential_variance

</> 
pub fn exponential_variance(lambda: Float) -> Result(
  Float,
  String,
)

Analytically compute the variance of a continuous exponential random variable
with given rate parameter $$\lambda \in (0, +\infty)$$.

The variance returned is: $$\frac{1}{\lambda^{2}}$$.

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