Numeric.Probability.Moments

Documentation

data Moments a

The first four commonly used moments of a probability distribution.

Constructors

Moments

Fields

• mean :: a

  Mean or Expected Value \( \mu \). Defined as \( \mu = E[X] \).

• variance :: a

  Variance \( \sigma^2 \). Defined as \( \sigma^2 = E[(X - \mu)^2] \). Equal to \( \sigma^2 = E[X^2] - \mu^2 \).

• skewness :: a

  Skewness \( \gamma_1 \). Defined as \( \gamma_1 = E\left[\left(\frac{(X - \mu)}{\sigma}\right)^3 \right] \).

• kurtosis :: a

  Kurtosis \( \kappa \). Defined as \( \kappa = E\left[\left(\frac{(X - \mu)}{\sigma}\right)^4 \right] \).

  The kurtosis is bounded below: \( \kappa \geq \gamma_1^2 + 1 \).

Instances

Show a => Show (Moments a)

Defined in Numeric.Probability.Moments

Methods

showsPrec :: Int -> Moments a -> ShowS

show :: Moments a -> String

showList :: [Moments a] -> ShowS

Eq a => Eq (Moments a)

Defined in Numeric.Probability.Moments

Methods

(==) :: Moments a -> Moments a -> Bool

(/=) :: Moments a -> Moments a -> Bool

fromExpectedPowers :: (Ord a, Num a, Fractional a) => (a, a, a, a) -> Moments a

Compute the Moments of a probability distribution given the expectation values of the first four powers \( m_k = E[X^k] \).

fromExpectedPowers (m1,m2,m3,m4)