gleam_stats - v1.1.0

gleam_stats/distributions/weibull

Functions related to continuous Weibull random variables.

Functions

do_weibull_cdf

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pub fn do_weibull_cdf(x: Float, lambda: Float, k: Float) -> Result(
  Float,
  String,
)

weibull_cdf

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pub fn weibull_cdf(x: Float, lambda: Float, k: Float) -> Result(
  Float,
  String,
)

Evaluate, at a certain point $$x \in (-\infty, +\infty)$$, the cumulative distribution function (cdf) of a Weibull random variable with scale parameter $$\lambda in (0, +\infty)$$ and shape parameter $$k \in (0, +\infty)$$.

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

 pub fn example() {
   let lambda: Float = 1.
   let k: Float = 5.
   // For illustrational purposes, evaluate the cdf at the 
   // point -100.0
   weibull.weibull_cdf(-100.0, lambda, k) 
   |> should.equal(Ok(0.0))
 }

weibull_mean

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pub fn weibull_mean(lambda: Float, k: Float) -> Result(
  Float,
  String,
)

Analytically compute the mean of a continuous Weibull random variable
with scale parameter $$\lambda \in (0, +\infty)$$ and shape parameter $$k \in (0, +\infty)$$.

The mean returned is: $$\lambda \cdot \Gamma\left(1 + \frac{1}{k}\right)$$.

weibull_pdf

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pub fn weibull_pdf(x: Float, lambda: Float, k: Float) -> Result(
  Float,
  String,
)

Evaluate, at a certain point $$x \in [0, +\infty)$$, the probability density function (pdf) of a continuous Weibull random variable with scale parameter $$\lambda in (0,+\infty)$$ and shape parameter $$k \in (0, +\infty)$$.

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

 pub fn example() {
   let lambda: Float = 1.
   let k: Float = 5.
   // For illustrational purposes, evaluate the pdf at the 
   // point -100.0
   weibull.weibull_pdf(-100.0, lambda, k) 
   |> should.equal(Ok(0.0))
 }

weibull_random

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pub fn weibull_random(stream: Iterator(Int), lambda: Float, k: Float, m: Int) -> Result(
  #(List(Float), Iterator(Int)),
  String,
)

Generate $$m \in \mathbb{Z}_{>0}$$ random numbers from a continuous Weibull distribution with scale parameter $$\lambda \in (0, +\infty)$$ and shape parameter $$k \in (0, +\infty)$$.

The random numbers are generated using the inverse transform method.

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

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

weibull_variance

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pub fn weibull_variance(lambda: Float, k: Float) -> Result(
  Float,
  String,
)

Analytically compute the variance of a continuous Weibull random variable
with scale parameter $$\lambda \in (0, +\infty)$$ and shape parameter $$k \in (0, +\infty)$$.

The variance returned is: $$\lambda^{2} \cdot \left[ \Gamma\left(1 + \frac{2}{k}\right) - \left(\Gamma\left(1 + \frac{1}{k}\right)\right)^{2} \right]$$.

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