GammaDistribution
org.apache.commons.math3.distribution

Class GammaDistribution

    • Field Detail

      • DEFAULT_INVERSE_ABSOLUTE_ACCURACY

        public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
        Default inverse cumulative probability accuracy.
        See Also:
        Constant Field Values
    • Constructor Detail

      • GammaDistribution

        public GammaDistribution(double shape,                 double scale)                  throws NotStrictlyPositiveException
        Creates a new gamma distribution with specified values of the shape and scale parameters.
        Parameters:
        shape - the shape parameter
        scale - the scale parameter
        Throws:
        NotStrictlyPositiveException - if shape <= 0 or scale <= 0.
      • GammaDistribution

        public GammaDistribution(double shape,                 double scale,                 double inverseCumAccuracy)                  throws NotStrictlyPositiveException
        Creates a new gamma distribution with specified values of the shape and scale parameters.
        Parameters:
        shape - the shape parameter
        scale - the scale parameter
        inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
        Throws:
        NotStrictlyPositiveException - if shape <= 0 or scale <= 0.
    • Method Detail

      • getAlpha

        @Deprecatedpublic double getAlpha()
        Deprecated. as of version 3.1, getShape() should be preferred. This method will be removed in version 4.0.
        Returns the shape parameter of this distribution.
        Returns:
        the shape parameter
      • getShape

        public double getShape()
        Returns the shape parameter of this distribution.
        Returns:
        the shape parameter
      • getBeta

        @Deprecatedpublic double getBeta()
        Deprecated. as of version 3.1, getScale() should be preferred. This method will be removed in version 4.0.
        Returns the scale parameter of this distribution.
        Returns:
        the scale parameter
      • getScale

        public double getScale()
        Returns the scale parameter of this distribution.
        Returns:
        the scale parameter
      • density

        public double density(double x)
        Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.
        Parameters:
        x - the point at which the PDF is evaluated
        Returns:
        the value of the probability density function at point x
      • logDensity

        public double logDensity(double x)
        Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double). The default implementation simply computes the logarithm of density(x).
        Overrides:
        logDensity in class AbstractRealDistribution
        Parameters:
        x - the point at which the PDF is evaluated
        Returns:
        the logarithm of the value of the probability density function at point x
      • cumulativeProbability

        public double cumulativeProbability(double x)
        For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. The implementation of this method is based on:
        • Chi-Squared Distribution, equation (9).
        • Casella, G., & Berger, R. (1990). Statistical Inference. Belmont, CA: Duxbury Press.
        Parameters:
        x - the point at which the CDF is evaluated
        Returns:
        the probability that a random variable with this distribution takes a value less than or equal to x
      • getNumericalMean

        public double getNumericalMean()
        Use this method to get the numerical value of the mean of this distribution. For shape parameter alpha and scale parameter beta, the mean is alpha * beta.
        Returns:
        the mean or Double.NaN if it is not defined
      • getNumericalVariance

        public double getNumericalVariance()
        Use this method to get the numerical value of the variance of this distribution. For shape parameter alpha and scale parameter beta, the variance is alpha * beta^2.
        Returns:
        the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined
      • getSupportLowerBound

        public double getSupportLowerBound()
        Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

        inf {x in R | P(X <= x) > 0}.

        The lower bound of the support is always 0 no matter the parameters.
        Returns:
        lower bound of the support (always 0)
      • getSupportUpperBound

        public double getSupportUpperBound()
        Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

        inf {x in R | P(X <= x) = 1}.

        The upper bound of the support is always positive infinity no matter the parameters.
        Returns:
        upper bound of the support (always Double.POSITIVE_INFINITY)
      • isSupportLowerBoundInclusive

        public boolean isSupportLowerBoundInclusive()
        Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.
        Returns:
        true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there
      • isSupportUpperBoundInclusive

        public boolean isSupportUpperBoundInclusive()
        Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.
        Returns:
        true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there
      • isSupportConnected

        public boolean isSupportConnected()
        Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
        Returns:
        true
      • sample

        public double sample()

        This implementation uses the following algorithms:

        For 0 < shape < 1:
        Ahrens, J. H. and Dieter, U., Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing, 12, 223-246, 1974.

        For shape >= 1:
        Marsaglia and Tsang, A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, Volume 26 Issue 3, September, 2000.

        Specified by:
        sample in interface RealDistribution
        Overrides:
        sample in class AbstractRealDistribution
        Returns:
        random value sampled from the Gamma(shape, scale) distribution

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