org.hipparchus.distribution.discrete

## Class AbstractIntegerDistribution

• java.lang.Object
• org.hipparchus.distribution.discrete.AbstractIntegerDistribution
• ### Constructor Summary

Constructors
Constructor and Description
AbstractIntegerDistribution()
• ### Method Summary

All Methods
Modifier and Type Method and Description
int inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
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.
double probability(int x0, int x1)
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
protected int solveInverseCumulativeProbability(double p, int lower, int upper)
This is a utility function used by inverseCumulativeProbability(double).
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface org.hipparchus.distribution.IntegerDistribution

cumulativeProbability, getNumericalMean, getNumericalVariance, getSupportLowerBound, getSupportUpperBound, isSupportConnected, probability
• ### Constructor Detail

• #### AbstractIntegerDistribution

public AbstractIntegerDistribution()
• ### Method Detail

• #### probability

public double probability(int x0,
int x1)
throws MathIllegalArgumentException
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity

P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

Specified by:
probability in interface IntegerDistribution
Parameters:
x0 - the exclusive lower bound
x1 - the inclusive upper bound
Returns:
the probability that a random variable with this distribution will take a value between x0 and x1, excluding the lower and including the upper endpoint
Throws:
MathIllegalArgumentException - if x0 > x1
• #### inverseCumulativeProbability

public int 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 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
Specified by:
inverseCumulativeProbability in interface IntegerDistribution
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
• #### solveInverseCumulativeProbability

protected int solveInverseCumulativeProbability(double p,
int lower,
int upper)
This is a utility function used by inverseCumulativeProbability(double). It assumes 0 < p < 1 and that the inverse cumulative probability lies in the bracket (lower, upper]. The implementation does simple bisection to find the smallest p-quantile inf{x in Z | P(X<=x) >= p}.
Parameters:
p - the cumulative probability
lower - a value satisfying cumulativeProbability(lower) < p
upper - a value satisfying p <= cumulativeProbability(upper)
Returns:
the smallest p-quantile of this distribution
• #### 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).

Specified by:
logProbability in interface IntegerDistribution
Parameters:
x - the point at which the PMF is evaluated
Returns:
the logarithm of the value of the probability mass function at x