Package com.opengamma.strata.math.impl.statistics.distribution

Class ChiSquareDistribution

  • All Implemented Interfaces:
    ProbabilityDistribution<Double>
    public class ChiSquareDistribution
extends Object
implements ProbabilityDistribution<Double>
    A $\chi^2$ distribution with $k$ degrees of freedom is the distribution of the sum of squares of $k$ independent standard normal random variables with cdf and inverse cdf $$ \begin{align*} F(x) &=\frac{\gamma\left(\frac{k}{2}, \frac{x}{2}\right)}{\Gamma\left(\frac{k}{2}\right)}\\ F^{-1}(p) &= 2\gamma^{-1}\left(\frac{k}{2}, p\right) \end{align*} $$ where $\gamma(y, z)$ is the lower incomplete Gamma function and $\Gamma(y)$ is the Gamma function. The pdf is given by: $$ \begin{align*} f(x)=\frac{x^{\frac{k}{2}-1}e^{-\frac{x}{2}}}{2^{\frac{k}{2}}\Gamma\left(\frac{k}{2}\right)} \end{align*} $$

    • Constructor Detail

      • ChiSquareDistribution

        public ChiSquareDistribution​(double degrees)
        Creates an instance.
        Parameters:
        degrees - The degrees of freedom of the distribution, not less than one

      • ChiSquareDistribution

        public ChiSquareDistribution​(double degrees,
                             RandomEngine engine)
        Creates an instance.
        Parameters:
        degrees - The degrees of freedom of the distribution, not less than one
        engine - A uniform random number generator, not null

    • Method Detail

      • getCDF

        public double getCDF​(Double x)
        Returns the cumulative distribution function for a value
        Specified by:
        getCDF in interface ProbabilityDistribution<Double>
        Parameters:
        x - The value, not null
        Returns:
        The cdf

      • getPDF

        public double getPDF​(Double x)
        Return the probability density function for a value
        Specified by:
        getPDF in interface ProbabilityDistribution<Double>
        Parameters:
        x - The value, not null
        Returns:
        The pdf

      • getInverseCDF

        public double getInverseCDF​(Double p)
        Given a probability, return the value that returns this cdf
        Specified by:
        getInverseCDF in interface ProbabilityDistribution<Double>
        Parameters:
        p - The probability, not null. $0 \geq p \geq 1$
        Returns:
        The inverse cdf

      • getDegreesOfFreedom

        public double getDegreesOfFreedom()
        Gets the degrees of freedom.
        Returns:
        The number of degrees of freedom

      • hashCode

        public int hashCode()
        Overrides:
        hashCode in class Object