Package org.hipparchus.distribution.continuous

Class NormalDistribution

java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.NormalDistribution
All Implemented Interfaces:
Serializable, RealDistribution
public class NormalDistribution extends AbstractRealDistribution
Implementation of the normal (gaussian) distribution.
See Also:

  • Constructor Details

    • NormalDistribution

      public NormalDistribution()
      Create a normal distribution with mean equal to zero and standard deviation equal to one.

    • NormalDistribution

      public NormalDistribution(double mean, double sd) throws MathIllegalArgumentException
      Create a normal distribution using the given mean, standard deviation.
      Parameters:
      mean - Mean for this distribution.
      sd - Standard deviation for this distribution.
      Throws:
      MathIllegalArgumentException - if sd <= 0.

  • Method Details

    • getMean

      public double getMean()
      Access the mean.
      Returns:
      the mean for this distribution.

    • getStandardDeviation

      public double getStandardDeviation()
      Access the standard deviation.
      Returns:
      the standard deviation for this distribution.

    • 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).

      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. If x is more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is within Double.MIN_VALUE of 0 or 1.
      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

    • inverseCumulativeProbability

      public double inverseCumulativeProbability(double p) throws MathIllegalArgumentException
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
      • inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(X<=x) > 0} for p = 0.
      The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface RealDistribution
      Overrides:
      inverseCumulativeProbability in class AbstractRealDistribution
      Parameters:
      p - the cumulative probability
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
      Throws:
      MathIllegalArgumentException - if p < 0 or p > 1

    • 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 mean parameter mu, the mean is mu.
      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 standard deviation parameter s, the variance is 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 negative infinity no matter the parameters.
      Returns:
      lower bound of the support (always Double.NEGATIVE_INFINITY)

    • 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