Class AbstractIntegerDistribution
- java.lang.Object
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- org.hipparchus.distribution.discrete.AbstractIntegerDistribution
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- All Implemented Interfaces:
Serializable
,IntegerDistribution
- Direct Known Subclasses:
BinomialDistribution
,EnumeratedIntegerDistribution
,GeometricDistribution
,HypergeometricDistribution
,PascalDistribution
,PoissonDistribution
,UniformIntegerDistribution
,ZipfDistribution
public abstract class AbstractIntegerDistribution extends Object implements IntegerDistribution, Serializable
Base class for integer-valued discrete distributions.Default implementations are provided for some of the methods that do not vary from distribution to distribution.
- See Also:
- Serialized Form
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Constructor Summary
Constructors Constructor Description AbstractIntegerDistribution()
Empty constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description int
inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.double
logProbability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
is the natural logarithm.double
probability(int x0, int x1)
For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.protected int
solveInverseCumulativeProbability(double p, int lower, int upper)
This is a utility function used byinverseCumulativeProbability(double)
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.hipparchus.distribution.IntegerDistribution
cumulativeProbability, getNumericalMean, getNumericalVariance, getSupportLowerBound, getSupportUpperBound, isSupportConnected, probability
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Method Detail
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probability
public double probability(int x0, int x1) throws MathIllegalArgumentException
For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
. The default implementation uses the identityP(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
- Specified by:
probability
in interfaceIntegerDistribution
- Parameters:
x0
- the exclusive lower boundx1
- the inclusive upper bound- Returns:
- the probability that a random variable with this distribution
will take a value between
x0
andx1
, excluding the lower and including the upper endpoint - Throws:
MathIllegalArgumentException
- ifx0 > x1
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inverseCumulativeProbability
public int inverseCumulativeProbability(double p) throws MathIllegalArgumentException
Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value isinf{x in Z | P(X<=x) >= p}
for0 < p <= 1
,inf{x in Z | P(X<=x) > 0}
forp = 0
.
int
, thenInteger.MIN_VALUE
orInteger.MAX_VALUE
is returned. The default implementation returnsIntegerDistribution.getSupportLowerBound()
forp = 0
,IntegerDistribution.getSupportUpperBound()
forp = 1
, andsolveInverseCumulativeProbability(double, int, int)
for0 < p < 1
.
- Specified by:
inverseCumulativeProbability
in interfaceIntegerDistribution
- Parameters:
p
- the cumulative probability- Returns:
- the smallest
p
-quantile of this distribution (largest 0-quantile forp = 0
) - Throws:
MathIllegalArgumentException
- ifp < 0
orp > 1
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solveInverseCumulativeProbability
protected int solveInverseCumulativeProbability(double p, int lower, int upper)
This is a utility function used byinverseCumulativeProbability(double)
. It assumes0 < p < 1
and that the inverse cumulative probability lies in the bracket(lower, upper]
. The implementation does simple bisection to find the smallestp
-quantileinf{x in Z | P(X<=x) >= p}
.- Parameters:
p
- the cumulative probabilitylower
- a value satisfyingcumulativeProbability(lower) < p
upper
- a value satisfyingp <= cumulativeProbability(upper)
- Returns:
- the smallest
p
-quantile of this distribution
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logProbability
public double logProbability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
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 ofIntegerDistribution.probability(int)
.The default implementation simply computes the logarithm of
probability(x)
.- Specified by:
logProbability
in interfaceIntegerDistribution
- Parameters:
x
- the point at which the PMF is evaluated- Returns:
- the logarithm of the value of the probability mass function at
x
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