gleam_stats/distributions/normal
Functions related to continuous normal random variables.
- Available functions
Functions
pub fn normal_cdf(x: Float, mu: Float, sigma: Float) -> Result(
Float,
String,
)
Evaluate, at a certain point $$x \in (-\infty, \infty)$$, the cumulative distribution function (cdf) of a continuous normal random variable with mean $$\mu \in (-\infty, +\infty)$$ and standard deviation $$\sigma\in (-\infty, +\infty)$$.
The cdf is defined as:
\[ F(x; \mu, \sigma) = \frac{1}{2} \cdot \left[ 1 + \text{erf}\left(\frac{x - \mu}{\sigma \cdot 2^{\frac{1}{2}}}\right) \right] \]
In the formula $$\text{erf}(\dot)$$ is the error function.
Example:
import gleam_stats/distributions/normal
import gleeunit/should
pub fn example() {
let mean: Float = 0.
let sigma: Float = 1.
// For illustrational purposes, evaluate the cdf at the
// point -100.0
normal.normal_cdf(-100.0, mu, sigma)
|> should.equal(Ok(0.0))
}
pub fn normal_mean(mu: Float, sigma: Float) -> Result(
Float,
String,
)
Analytically compute the mean of a continuous normal random variable
with given mean $$\mu \in (-\infty, +\infty)$$ and standard deviation
$$\sigma \in (-\infty, +\infty)$$ .
The mean returned is: $$\mu$$.
pub fn normal_pdf(x: Float, mu: Float, sigma: Float) -> Result(
Float,
String,
)
Evaluate, at a certain point $$x \in (-\infty, +\infty)$$, the probability density function (pdf) of a continuous normal random variable with given mean $$\mu \in (-\infty, +\infty)$$ and standard deviation $$\sigma\in (-\infty, +\infty)$$ .
The pdf is defined as:
\[ f(x; \mu, \sigma) = \frac{1}{\sigma \cdot \left(2 \cdot \pi \right)^{\frac{1}{2}}} \cdot e^{- \frac{1}{2} \cdot \left(\frac{x - \mu}{\sigma}\right)^{2}} \]
Example:
import gleam_stats/distributions/normal
import gleeunit/should
pub fn example() {
let mean: Float = 0.
let sigma: Float = 1.
// For illustrational purposes, evaluate the pdf at the
// point -100.0
normal.normal_pdf(-100.0, mu, sigma)
|> should.equal(Ok(0.0))
}
pub fn normal_random(stream: Iterator(Int), mu: Float, sigma: Float, m: Int) -> Result(
#(List(Float), Iterator(Int)),
String,
)
Generate $$m \in \in \mathbb{Z}_{>0}$$ random numbers from a continuous normal distribution with a given mean $$\mu \in (-\infty, +\infty)$$ and standard deviation $$\sigma\in (-\infty, +\infty)$$.
The random numbers are generated using Box–Muller transform.
Example:
import gleam/iterator.{Iterator}
import gleam_stats/generators
import gleam_stats/distributions/normal
pub fn example() {
let seed: Int = 5
let seq: Int = 1
let mean: Float = 0.
let std: Float = 1.
assert Ok(out) =
generators.seed_pcg32(seed, seq)
|> normal.normal_random(mean, std, 5_000)
let rands: List(Float) = pair.first(out)
let stream: Iterator(Int) = pair.second(out)
}
pub fn normal_variance(mu: Float, sigma: Float) -> Result(
Float,
String,
)
Analytically compute the variance of a continuous normal random variable
with given mean $$\mu \in (-\infty, +\infty)$$ and standard deviation
$$\sigma\in (-\infty, +\infty)$$ .
The variance returned is: $$\sigma^{2}$$.