statistics-0.4.1: A library of statistical types, data, and functions

Portabilityportable
Stabilityexperimental
Maintainerbos@serpentine.com

Statistics.Distribution

Description

Types and functions common to many probability distributions.

Synopsis

Documentation

class Distribution d whereSource

The interface shared by all probability distributions.

Methods

density :: d -> Double -> DoubleSource

Probability density function. The probability that a the random variable X has the value x, i.e. P(X=x).

cumulative :: d -> Double -> DoubleSource

Cumulative distribution function. The probability that a random variable X is less than x, i.e. P(Xx).

quantile :: d -> Double -> DoubleSource

Inverse of the cumulative distribution function. The value x for which P(Xx).

findRootSource

Arguments

:: Distribution d 
=> d 
-> Double

Probability p

-> Double

Initial guess

-> Double

Lower bound on interval

-> Double

Upper bound on interval

-> Double 

Approximate the value of X for which P(x>X)=p.

This method uses a combination of Newton-Raphson iteration and bisection with the given guess as a starting point. The upper and lower bounds specify the interval in which the probability distribution reaches the value p.