Documentation of 'smile.stat.distribution.ChiSquareDistribution' Java class
ChiSquareDistribution
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smile.stat.distribution

Class ChiSquareDistribution

  • All Implemented Interfaces:
    Distribution, ExponentialFamily

    public class ChiSquareDistribution
extends AbstractDistribution
implements ExponentialFamily
    Chi-square (or chi-squared) distribution with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It's mean and variance are k and 2k, respectively. The chi-square distribution is a special case of the gamma distribution. It follows from the definition of the chi-square distribution that the sum of independent chi-square variables is also chi-square distributed. Specifically, if Xi are independent chi-square variables with ki degrees of freedom, respectively, then Y = Σ Xi is chi-square distributed with Σ ki degrees of freedom.

    The chi-square distribution has numerous applications in inferential statistics, for instance in chi-square tests and in estimating variances. Many other statistical tests also lead to a use of this distribution, like Friedman's analysis of variance by ranks.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double cdf(double x)
      Cumulative distribution function.
      double entropy()
      Shannon entropy of the distribution.
      int getNu()
      Returns the parameter nu, the degrees of freedom.
      double logp(double x)
      The density at x in log scale, which may prevents the underflow problem.
      Mixture.Component M(double[] x, double[] posteriori)
      The M step in the EM algorithm, which depends the specific distribution.
      double mean()
      The mean of distribution.
      int npara()
      The number of parameters of the distribution.
      double p(double x)
      The probability density function for continuous distribution or probability mass function for discrete distribution at x.
      double quantile(double p)
      The quantile, the probability to the left of quantile is p.
      double rand()
      Generates a random number following this distribution.
      double sd()
      The standard deviation of distribution.
      java.lang.String toString() 
      double var()
      The variance of distribution.

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

    • Constructor Detail

      • ChiSquareDistribution

        public ChiSquareDistribution(int nu)
        Constructor.
        Parameters:
        nu - the degree of freedom.

    • Method Detail

      • getNu

        public int getNu()
        Returns the parameter nu, the degrees of freedom.

      • npara

        public int npara()
        Description copied from interface: Distribution
        The number of parameters of the distribution.
        Specified by:
        npara in interface Distribution

      • mean

        public double mean()
        Description copied from interface: Distribution
        The mean of distribution.
        Specified by:
        mean in interface Distribution

      • var

        public double var()
        Description copied from interface: Distribution
        The variance of distribution.
        Specified by:
        var in interface Distribution

      • sd

        public double sd()
        Description copied from interface: Distribution
        The standard deviation of distribution.
        Specified by:
        sd in interface Distribution

      • entropy

        public double entropy()
        Description copied from interface: Distribution
        Shannon entropy of the distribution.
        Specified by:
        entropy in interface Distribution

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object

      • rand

        public double rand()
        Description copied from interface: Distribution
        Generates a random number following this distribution.
        Specified by:
        rand in interface Distribution

      • p

        public double p(double x)
        Description copied from interface: Distribution
        The probability density function for continuous distribution or probability mass function for discrete distribution at x.
        Specified by:
        p in interface Distribution

      • logp

        public double logp(double x)
        Description copied from interface: Distribution
        The density at x in log scale, which may prevents the underflow problem.
        Specified by:
        logp in interface Distribution

      • cdf

        public double cdf(double x)
        Description copied from interface: Distribution
        Cumulative distribution function. That is the probability to the left of x.
        Specified by:
        cdf in interface Distribution

      • quantile

        public double quantile(double p)
        Description copied from interface: Distribution
        The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.
        Specified by:
        quantile in interface Distribution

      • M

        public Mixture.Component M(double[] x,
                           double[] posteriori)
        Description copied from interface: ExponentialFamily
        The M step in the EM algorithm, which depends the specific distribution.
        Specified by:
        M in interface ExponentialFamily
        Parameters:
        x - the input data for estimation
        posteriori - the posteriori probability.
        Returns:
        the (unnormalized) weight of this distribution in the mixture.
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