Class GeometricDistribution
- All Implemented Interfaces:
DiscreteDistribution
The probability mass function of \( X \) is:
\[ f(k; p) = (1-p)^k \, p \]
for \( p \in (0, 1] \) the probability of success and \( k \in \{0, 1, 2, \dots\} \) the number of failures.
This parameterization is used to model the number of failures until the first success.
- 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 static final double
1/2.private final double
log(1 - p)
where p is the probability of success.private final double
log(p)
where p is the probability of success.private final IntToDoubleFunction
Implementation of PMF(x).private final double
The probability of success.private final double
Value of survival probability for x=0. -
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.double
Gets the probability of success parameter 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 GeometricDistribution
of
(double p) Creates a geometric distribution.double
probability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
.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, probability
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Field Details
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HALF
private static final double HALF1/2.- See Also:
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probabilityOfSuccess
private final double probabilityOfSuccessThe probability of success. -
logProbabilityOfSuccess
private final double logProbabilityOfSuccesslog(p)
where p is the probability of success. -
log1mProbabilityOfSuccess
private final double log1mProbabilityOfSuccesslog(1 - p)
where p is the probability of success. -
sf0
private final double sf0Value of survival probability for x=0. Used in the survival functions. Equal to (1 - probability of success). -
pmf
Implementation of PMF(x). Assumes thatx > 0
.
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Constructor Details
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GeometricDistribution
private GeometricDistribution(double p) - Parameters:
p
- Probability of success.
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Method Details
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of
Creates a geometric distribution.- Parameters:
p
- Probability of success.- Returns:
- the geometric distribution
- Throws:
IllegalArgumentException
- ifp <= 0
orp > 1
.
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getProbabilityOfSuccess
public double getProbabilityOfSuccess()Gets the probability of success parameter of this distribution.- Returns:
- the probability of success.
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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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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 probability parameter \( p \), the mean is:
\[ \frac{1 - p}{p} \]
- Returns:
- the mean.
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getVariance
public double getVariance()Gets the variance of this distribution.For probability parameter \( p \), the variance is:
\[ \frac{1 - p}{p^2} \]
- 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 always 0.
- Returns:
- 0.
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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 positive infinity except for the probability parameter
p = 1.0
.- Returns:
Integer.MAX_VALUE
or 0.
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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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