Class UniformDiscreteDistribution
- All Implemented Interfaces:
DiscreteDistribution
The probability mass function of \( X \) is:
\[ f(k; a, b) = \frac{1}{b-a+1} \]
for integer \( a, b \) and \( a \le b \) and \( k \in [a, b] \).
- See Also:
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Nested Class Summary
Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution
DiscreteDistribution.Sampler
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate final double
Cache of the log probability.private final int
Lower bound (inclusive) of this distribution.private final double
Cache of the probability.private final double
Value of survival probability for x=0.private final int
Upper bound (inclusive) of this distribution.private final double
"upper" - "lower" + 1 (as a double to avoid overflow). -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptioncreateSampler
(org.apache.commons.rng.UniformRandomProvider rng) Creates a sampler.double
cumulativeProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
getMean()
Gets the mean of this distribution.int
Gets the lower bound of the support.int
Gets the upper bound of the support.double
Gets the variance of this distribution.int
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.int
inverseSurvivalProbability
(double p) Computes the inverse survival probability 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.static UniformDiscreteDistribution
of
(int lower, int upper) Creates a new uniform discrete distribution.double
probability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
.double
probability
(int x0, int x1) For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.double
survivalProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X > x)
.Methods inherited from class org.apache.commons.statistics.distribution.AbstractDiscreteDistribution
getMedian
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Field Details
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lower
private final int lowerLower bound (inclusive) of this distribution. -
upper
private final int upperUpper bound (inclusive) of this distribution. -
upperMinusLowerPlus1
private final double upperMinusLowerPlus1"upper" - "lower" + 1 (as a double to avoid overflow). -
pmf
private final double pmfCache of the probability. -
logPmf
private final double logPmfCache of the log probability. -
sf0
private final double sf0Value of survival probability for x=0. Used in the inverse survival function.
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Constructor Details
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UniformDiscreteDistribution
private UniformDiscreteDistribution(int lower, int upper) - Parameters:
lower
- Lower bound (inclusive) of this distribution.upper
- Upper bound (inclusive) of this distribution.
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Method Details
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of
Creates a new uniform discrete distribution.- Parameters:
lower
- Lower bound (inclusive) of this distribution.upper
- Upper bound (inclusive) of this distribution.- Returns:
- the distribution
- Throws:
IllegalArgumentException
- iflower > upper
.
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probability
public double probability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
. In other words, this method represents the probability mass function (PMF) for the distribution.- Parameters:
x
- Point at which the PMF is evaluated.- Returns:
- the value of the probability mass function at
x
.
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probability
public double probability(int x0, int x1) 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)
Special cases:
- returns
0.0
ifx0 == x1
; - returns
probability(x1)
ifx0 + 1 == x1
;
- Specified by:
probability
in interfaceDiscreteDistribution
- Overrides:
probability
in classAbstractDiscreteDistribution
- Parameters:
x0
- Lower bound (exclusive).x1
- Upper bound (inclusive).- Returns:
- the probability that a random variable with this distribution
takes a value between
x0
andx1
, excluding the lower and including the upper endpoint.
- returns
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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.- Parameters:
x
- Point at which the PMF is evaluated.- Returns:
- the logarithm of the value of the probability mass function at
x
.
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cumulativeProbability
public double cumulativeProbability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
. In other, words, this method represents the (cumulative) distribution function (CDF) for this distribution.- Parameters:
x
- 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
.
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survivalProbability
public double survivalProbability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X > x)
. In other words, this method represents the complementary cumulative distribution function.By default, this is defined as
1 - cumulativeProbability(x)
, but the specific implementation may be more accurate.- Parameters:
x
- Point at which the survival function is evaluated.- Returns:
- the probability that a random variable with this
distribution takes a value greater than
x
.
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inverseCumulativeProbability
public int inverseCumulativeProbability(double p) Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases} \]
If the result exceeds the range of the data type
int
, thenInteger.MIN_VALUE
orInteger.MAX_VALUE
is returned. In this case the result ofcumulativeProbability(x)
called using the returnedp
-quantile may not compute the originalp
.The default implementation returns:
DiscreteDistribution.getSupportLowerBound()
forp = 0
,DiscreteDistribution.getSupportUpperBound()
forp = 1
, or- the result of a binary search between the lower and upper bound using
cumulativeProbability(x)
. The bounds may be bracketed for efficiency.
- Specified by:
inverseCumulativeProbability
in interfaceDiscreteDistribution
- Overrides:
inverseCumulativeProbability
in classAbstractDiscreteDistribution
- Parameters:
p
- Cumulative probability.- Returns:
- the smallest
p
-quantile of this distribution (largest 0-quantile forp = 0
).
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inverseSurvivalProbability
public int inverseSurvivalProbability(double p) Computes the inverse survival probability function of this distribution. For a random variableX
distributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \ge x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb Z : P(X \ge x) \lt 1 \} & \text{for } p = 1 \end{cases} \]
If the result exceeds the range of the data type
int
, thenInteger.MIN_VALUE
orInteger.MAX_VALUE
is returned. In this case the result ofsurvivalProbability(x)
called using the returned(1-p)
-quantile may not compute the originalp
.By default, this is defined as
inverseCumulativeProbability(1 - p)
, but the specific implementation may be more accurate.The default implementation returns:
DiscreteDistribution.getSupportLowerBound()
forp = 1
,DiscreteDistribution.getSupportUpperBound()
forp = 0
, or- the result of a binary search between the lower and upper bound using
survivalProbability(x)
. The bounds may be bracketed for efficiency.
- Specified by:
inverseSurvivalProbability
in interfaceDiscreteDistribution
- Overrides:
inverseSurvivalProbability
in classAbstractDiscreteDistribution
- Parameters:
p
- Cumulative probability.- Returns:
- the smallest
(1-p)
-quantile of this distribution (largest 0-quantile forp = 1
).
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getMean
public double getMean()Gets the mean of this distribution.For lower bound \( a \) and upper bound \( b \), the mean is \( \frac{1}{2} (a + b) \).
- Returns:
- the mean.
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getVariance
public double getVariance()Gets the variance of this distribution.For lower bound \( a \) and upper bound \( b \), the variance is:
\[ \frac{1}{12} (n^2 - 1) \]
where \( n = b - a + 1 \).
- Returns:
- the variance.
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getSupportLowerBound
public int getSupportLowerBound()Gets the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
, i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} \). By convention,Integer.MIN_VALUE
should be substituted for negative infinity.The lower bound of the support is equal to the lower bound parameter of the distribution.
- Returns:
- the lower bound of the support.
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getSupportUpperBound
public int getSupportUpperBound()Gets the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
, i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) = 1 \} \). By convention,Integer.MAX_VALUE
should be substituted for positive infinity.The upper bound of the support is equal to the upper bound parameter of the distribution.
- Returns:
- the upper bound of the support.
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createSampler
Creates a sampler.- Specified by:
createSampler
in interfaceDiscreteDistribution
- Overrides:
createSampler
in classAbstractDiscreteDistribution
- Parameters:
rng
- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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