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

Safe HaskellNone




Types classes for probability distrubutions


Type classes

class Distribution d whereSource

Type class common to all distributions. Only c.d.f. could be defined for both discrete and continous distributions.


cumulative :: d -> Double -> DoubleSource

Cumulative distribution function. The probability that a random variable X is less or equal than x, i.e. P(Xx). Cumulative should be defined for infinities as well:

 cumulative d +∞ = 1
 cumulative d -∞ = 0

complCumulative :: d -> Double -> DoubleSource

One's complement of cumulative distibution:

 complCumulative d x = 1 - cumulative d x

It's useful when one is interested in P(X<x) and expression on the right side begin to lose precision. This function have default implementation but implementors are encouraged to provide more precise implementation.

class Distribution d => ContDistr d whereSource

Continuous probability distributuion


density :: d -> Double -> DoubleSource

Probability density function. Probability that random variable X lies in the infinitesimal interval [x,x+δx) equal to density(x)⋅δx

quantile :: d -> Double -> DoubleSource

Inverse of the cumulative distribution function. The value x for which P(Xx) = p. If probability is outside of [0,1] range function should call error

Distribution statistics

class MaybeMean d => Mean d whereSource

Type class for distributions with mean. If distribution have finite mean for all valid values of parameters it should be instance of this type class.


mean :: d -> DoubleSource

class (Mean d, MaybeVariance d) => Variance d whereSource

Type class for distributions with variance. If distibution have finite variance for all valid parameter values it should be instance of this type class.

Minimal complete definition is variance or stdDev

Random number generation

class (DiscreteDistr d, ContGen d) => DiscreteGen d whereSource

Generate discrete random variates which have given distribution. ContGen is superclass because it's always possible to generate real-valued variates from integer values


genDiscreteVar :: PrimMonad m => d -> Gen (PrimState m) -> m IntSource

genContinous :: (ContDistr d, PrimMonad m) => d -> Gen (PrimState m) -> m DoubleSource

Generate variates from continous distribution using inverse transform rule.

Helper functions



:: ContDistr 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.

sumProbabilities :: DiscreteDistr d => d -> Int -> Int -> DoubleSource

Sum probabilities in inclusive interval.