Statistics.Distribution

Types and functions common to many probability distributions.

Documentation

class Distribution d where

The interface shared by all probability distributions.

Methods

probability :: d -> Double -> Double

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

cumulative :: d -> Double -> Double

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

inverse :: d -> Double -> Double

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

Instances

Distribution GeometricDistribution

Distribution ExponentialDistribution

Distribution NormalDistribution

Distribution BinomialDistribution

Distribution GammaDistribution

Distribution HypergeometricDistribution

Distribution PoissonDistribution

class Distribution d => Mean d where

Methods

mean :: d -> Double

Instances

Mean GeometricDistribution

Mean ExponentialDistribution

Mean NormalDistribution

Mean BinomialDistribution

Mean GammaDistribution

Mean HypergeometricDistribution

Mean PoissonDistribution

class Mean d => Variance d where

Methods

variance :: d -> Double

Instances

Variance GeometricDistribution

Variance ExponentialDistribution

Variance NormalDistribution

Variance BinomialDistribution

Variance GammaDistribution

Variance HypergeometricDistribution

Variance PoissonDistribution

findRoot

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.