Constructor Detail

• GeometricDistribution

  public GeometricDistribution(double p)

  Create a geometric distribution with the given probability of success.

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

  p - probability of success.

  Throws:

  OutOfRangeException - if p <= 0 or p > 1.

• GeometricDistribution

  public GeometricDistribution(RandomGenerator rng,
                       double p)

  Creates a geometric distribution.

  Parameters:

  rng - Random number generator.

  p - Probability of success.

  Throws:

  OutOfRangeException - if p <= 0 or p > 1.

Method Detail

• getProbabilityOfSuccess

  public double getProbabilityOfSuccess()

  Access the probability of success for this distribution.

  Returns:

  the probability of success.

• probability

  public double probability(int 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 probability mass function (PMF) for the distribution.

  Parameters:

  x - the point at which the PMF is evaluated

  Returns:

  the value of the probability mass function at x

• logProbability

  public double logProbability(int x)

  For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. 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 IntegerDistribution.probability(int).

  The default implementation simply computes the logarithm of probability(x).

  Overrides:

  logProbability in class AbstractIntegerDistribution

  Parameters:

  x - the point at which the PMF is evaluated

  Returns:

  the logarithm of the value of the probability mass function at x

• cumulativeProbability

  public double cumulativeProbability(int 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

• getNumericalMean

  public double getNumericalMean()

  Use this method to get the numerical value of the mean of this distribution. For probability parameter p, the mean is (1 - p) / p.

  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 probability parameter p, the variance is (1 - p) / (p * p).

  Returns:

  the variance (possibly Double.POSITIVE_INFINITY or Double.NaN if it is not defined)

• getSupportLowerBound

  public int 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 Z | P(X <= x) > 0}.

  The lower bound of the support is always 0.

  Returns:

  lower bound of the support (always 0)

• getSupportUpperBound

  public int 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 infinite (which we approximate as Integer.MAX_VALUE).

  Returns:

  upper bound of the support (always Integer.MAX_VALUE)

• isSupportConnected

  public boolean isSupportConnected()

  Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

  Returns:

  true

• inverseCumulativeProbability

  public int 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 Z | P(X<=x) >= p} for 0 < p <= 1,
  • inf{x in Z | P(X<=x) > 0} for p = 0.

  If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. The default implementation returns

  • IntegerDistribution.getSupportLowerBound() for p = 0,
  • IntegerDistribution.getSupportUpperBound() for p = 1, and
  • AbstractIntegerDistribution.solveInverseCumulativeProbability(double, int, int) for 0 < p < 1.

  Specified by:

  inverseCumulativeProbability in interface IntegerDistribution

  Overrides:

  inverseCumulativeProbability in class AbstractIntegerDistribution

  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