Class GammaDistribution

    • Field Detail

      • DEFAULT_INVERSE_ABSOLUTE_ACCURACY

        public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
        Default inverse cumulative probability accuracy.
        Since:
        2.1
        See Also:
        Constant Field Values
      • serialVersionUID

        private static final long serialVersionUID
        Serializable version identifier.
        See Also:
        Constant Field Values
      • shape

        private final double shape
        The shape parameter.
      • scale

        private final double scale
        The scale parameter.
      • shiftedShape

        private final double shiftedShape
        The constant value of shape + g + 0.5, where g is the Lanczos constant Gamma.LANCZOS_G.
      • densityPrefactor1

        private final double densityPrefactor1
        The constant value of shape / scale * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape), where L(shape) is the Lanczos approximation returned by Gamma.lanczos(double). This prefactor is used in density(double), when no overflow occurs with the natural calculation.
      • logDensityPrefactor1

        private final double logDensityPrefactor1
        The constant value of log(shape / scale * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape)), where L(shape) is the Lanczos approximation returned by Gamma.lanczos(double). This prefactor is used in logDensity(double), when no overflow occurs with the natural calculation.
      • densityPrefactor2

        private final double densityPrefactor2
        The constant value of shape * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape), where L(shape) is the Lanczos approximation returned by Gamma.lanczos(double). This prefactor is used in density(double), when overflow occurs with the natural calculation.
      • logDensityPrefactor2

        private final double logDensityPrefactor2
        The constant value of log(shape * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape)), where L(shape) is the Lanczos approximation returned by Gamma.lanczos(double). This prefactor is used in logDensity(double), when overflow occurs with the natural calculation.
      • minY

        private final double minY
        Lower bound on y = x / scale for the selection of the computation method in density(double). For y <= minY, the natural calculation overflows.
      • maxLogY

        private final double maxLogY
        Upper bound on log(y) (y = x / scale) for the selection of the computation method in density(double). For log(y) >= maxLogY, the natural calculation overflows.
      • solverAbsoluteAccuracy

        private final double solverAbsoluteAccuracy
        Inverse cumulative probability accuracy.
    • 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.

        Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

        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.

        Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

        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.
        Since:
        2.1
    • Method Detail

      • getAlpha

        @Deprecated
        public 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
        Since:
        3.1
      • getBeta

        @Deprecated
        public 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
        Since:
        3.1
      • 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
      • getSolverAbsoluteAccuracy

        protected double getSolverAbsoluteAccuracy()
        Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.
        Overrides:
        getSolverAbsoluteAccuracy in class AbstractRealDistribution
        Returns:
        the maximum absolute error in inverse cumulative probability estimates
      • 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