Constructor Detail

• LaplaceDistribution

  public LaplaceDistribution(double mu,
                     double beta)

  Build a new instance.

  Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.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:

  mu - location parameter

  beta - scale parameter (must be positive)

  Throws:

  NotStrictlyPositiveException - if beta <= 0

• LaplaceDistribution

  public LaplaceDistribution(RandomGenerator rng,
                     double mu,
                     double beta)

  Build a new instance.

  Parameters:

  rng - Random number generator

  mu - location parameter

  beta - scale parameter (must be positive)

  Throws:

  NotStrictlyPositiveException - if beta <= 0

Method Detail

• getLocation

  public double getLocation()

  Access the location parameter, mu.

  Returns:

  the location parameter.

• getScale

  public double getScale()

  Access the scale parameter, beta.

  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

• 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.

  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 OutOfRangeException

  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

  • RealDistribution.getSupportLowerBound() for p = 0,
  • RealDistribution.getSupportUpperBound() for p = 1.

  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:

  OutOfRangeException - if p < 0 or p > 1

• getNumericalMean

  public double getNumericalMean()

  Use this method to get the numerical value of the mean of this distribution.

  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.

  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}.

  Returns:

  lower bound of the support (might be 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}.

  Returns:

  upper bound of the support (might be 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.

  Returns:

  whether the support is connected or not