Probability & Distribution Domain

The Probability domain gives you tools for Statistical Distributions and structured randomness.

Standard random() just gives you a boring uniform number between 0 and 1. But reality isn't uniform.

• Heights of people follow a Bell Curve (Normal distribution).
• Radioactive decay follows a Poisson distribution.
• Success/failure rates follow a Bernoulli distribution.

This domain lets you define the shape of the chaotic world you want to simulate, and then draw mathematically correct samples from it.

Overview

use aivi.probability (Normal, uniform)

// Create a Bell curve centered at 0 with standard deviation of 1
distribution = Normal(0.0, 1.0) 

// Get a random number that fits this curve
// (Most values will be near 0, few will be near -3 or 3)
sample = distribution |> sample()

Features

Probability = Float
Distribution a = { pdf: a -> Probability }

Domain Definition

domain Probability over Probability = {
  (+) : Probability -> Probability -> Probability
  (-) : Probability -> Probability -> Probability
  (*) : Probability -> Probability -> Probability
}

Helper Functions

Function	Explanation
clamp p Probability -> Probability	Bounds p into [0.0, 1.0].
bernoulli p Probability -> Distribution Bool	Creates a distribution over Bool with success probability p.
uniform lo hi Float -> Float -> Distribution Float	Creates a uniform distribution over [lo, hi].
expectation dist x Distribution Float -> Float -> Float	Returns the contribution of x to the expected value.

Usage Examples

use aivi.probability

p = clamp 0.7
coin = bernoulli p
probHeads = coin.pdf true