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smile.stat.distribution

Class GaussianDistribution

    • Field Summary

      Fields 
      Modifier and Type Field and Description
      double mu
      The mean.
      double sigma
      The standard deviation.
    • Constructor Summary

      Constructors 
      Constructor and Description
      GaussianDistribution(double mu, double sigma)
      Constructor
    • Method Summary

      All Methods Static 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.
      static GaussianDistribution fit(double[] data)
      Estimates the distribution parameters by MLE.
      static GaussianDistribution getInstance() 
      double inverseCDF()
      Generates a Gaussian random number with the inverse CDF method.
      int length()
      The number of parameters of the distribution.
      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.
      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(p) is p.
      double rand()
      Generates a Gaussian random number with the Box-Muller algorithm.
      double sd()
      The standard deviation of distribution.
      java.lang.String toString() 
      double variance()
      The variance of distribution.
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
    • Field Detail

      • mu

        public final double mu
        The mean.
      • sigma

        public final double sigma
        The standard deviation.
    • Constructor Detail

      • GaussianDistribution

        public GaussianDistribution(double mu,
                                    double sigma)
        Constructor
        Parameters:
        mu - mean.
        sigma - standard deviation.
    • Method Detail

      • fit

        public static GaussianDistribution fit(double[] data)
        Estimates the distribution parameters by MLE.
      • length

        public int length()
        Description copied from interface: Distribution
        The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
        Specified by:
        length in interface Distribution
      • mean

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

        public double variance()
        Description copied from interface: Distribution
        The variance of distribution.
        Specified by:
        variance 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()
        Generates a Gaussian random number with the Box-Muller algorithm.
        Specified by:
        rand in interface Distribution
      • inverseCDF

        public double inverseCDF()
        Generates a Gaussian random number with the inverse CDF method.
      • 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)
        The quantile, the probability to the left of quantile(p) is p. This is actually the inverse of cdf. Original algorythm and Perl implementation can be found at: http://www.math.uio.no/~jacklam/notes/invnorm/index.html
        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.