Package org.hipparchus.distribution.continuous

Class LogNormalDistribution

  • All Implemented Interfaces:
    Serializable, RealDistribution
    public class LogNormalDistribution
extends AbstractRealDistribution
    Implementation of the log-normal (gaussian) distribution.

    Parameters: X is log-normally distributed if its natural logarithm log(X) is normally distributed. The probability distribution function of X is given by (for x > 0)

    exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)

    • m is the location parameter: this is the mean of the normally distributed natural logarithm of this distribution,
    • s is the shape parameter: this is the standard deviation of the normally distributed natural logarithm of this distribution.
    See Also:
    Log-normal distribution (Wikipedia), Log Normal distribution (MathWorld), Serialized Form

    • Constructor Detail

      • LogNormalDistribution

        public LogNormalDistribution()
        Create a log-normal distribution, where the mean and standard deviation of the normally distributed natural logarithm of the log-normal distribution are equal to zero and one respectively. In other words, the location of the returned distribution is 0, while its shape is 1.

      • LogNormalDistribution

        public LogNormalDistribution​(double location,
                             double shape)
                      throws MathIllegalArgumentException
        Create a log-normal distribution using the specified location and shape.
        Parameters:
        location - the location parameter of this distribution
        shape - the shape parameter of this distribution
        Throws:
        MathIllegalArgumentException - if shape <= 0.

      • LogNormalDistribution

        public LogNormalDistribution​(double location,
                             double shape,
                             double inverseCumAccuracy)
                      throws MathIllegalArgumentException
        Creates a log-normal distribution.
        Parameters:
        location - Location parameter of this distribution.
        shape - Shape parameter of this distribution.
        inverseCumAccuracy - Inverse cumulative probability accuracy.
        Throws:
        MathIllegalArgumentException - if shape <= 0.

    • Method Detail

      • getLocation

        public double getLocation()
        Returns the location parameter of this distribution.
        Returns:
        the location parameter
        Since:
        1.4

      • getShape

        public double getShape()
        Returns the shape parameter of this distribution.
        Returns:
        the shape 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. For location m, and shape s of this distribution, the PDF is given by
        • 0 if x <= 0,
        • exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x) otherwise.
        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). See documentation of density(double) for computation details.

        Specified by:
        logDensity in interface RealDistribution
        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. For location m, and shape s of this distribution, the CDF is given by
        • 0 if x <= 0,
        • 0 if ln(x) - m < 0 and m - ln(x) > 40 * s, as in these cases the actual value is within Double.MIN_VALUE of 0,
        • 1 if ln(x) - m >= 0 and ln(x) - m > 40 * s, as in these cases the actual value is within Double.MIN_VALUE of 1,
        • 0.5 + 0.5 * erf((ln(x) - m) / (s * sqrt(2)) otherwise.
        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

      • probability

        public double probability​(double x0,
                          double x1)
                   throws MathIllegalArgumentException
        For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
        Specified by:
        probability in interface RealDistribution
        Overrides:
        probability in class AbstractRealDistribution
        Parameters:
        x0 - Lower bound (excluded).
        x1 - Upper bound (included).
        Returns:
        the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.
        Throws:
        MathIllegalArgumentException - if x0 > x1. The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

      • getNumericalMean

        public double getNumericalMean()
        Use this method to get the numerical value of the mean of this distribution. For location m and shape s, the mean is exp(m + s^2 / 2).
        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 location m and shape s, the variance is (exp(s^2) - 1) * exp(2 * m + s^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)

      • 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