Class TDistribution.StudentsTDistribution
- java.lang.Object
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- org.apache.commons.statistics.distribution.AbstractContinuousDistribution
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- org.apache.commons.statistics.distribution.TDistribution
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- org.apache.commons.statistics.distribution.TDistribution.StudentsTDistribution
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- All Implemented Interfaces:
ContinuousDistribution
- Enclosing class:
- TDistribution
private static class TDistribution.StudentsTDistribution extends TDistribution
Implementation of Student's T-distribution.
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Nested Class Summary
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Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
ContinuousDistribution.Sampler
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Field Summary
Fields Modifier and Type Field Description private static double
CLOSE_TO_ZERO
The threshold for the density function where the power function base minus 1 is close to zero.private double
densityNormalisation
Density normalisation factor, sqrt(v) * beta(1/2, v/2), where v = degrees of freedom.private double
logDensityNormalisation
Log density normalisation term, 0.5 * log(v) + log(beta(1/2, v/2)), where v = degrees of freedom.private double
mean
Cached value for inverse probability function.private double
mvp1Over2
-(v + 1) / 2, where v = degrees of freedom.private static double
TWO
2.private double
variance
Cached value for inverse probability function.
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Constructor Summary
Constructors Constructor Description StudentsTDistribution(double degreesOfFreedom, double variance)
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description (package private) static double
computeVariance(double degreesOfFreedom)
ContinuousDistribution.Sampler
createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.double
cumulativeProbability(double x)
For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
.double
getMean()
Gets the mean of this distribution.(package private) double
getMedian()
Gets the median.double
getVariance()
Gets the variance of this distribution.double
logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
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Methods inherited from class org.apache.commons.statistics.distribution.TDistribution
getDegreesOfFreedom, getSupportLowerBound, getSupportUpperBound, inverseSurvivalProbability, of, survivalProbability
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Methods inherited from class org.apache.commons.statistics.distribution.AbstractContinuousDistribution
inverseCumulativeProbability, isSupportConnected, probability
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Field Detail
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TWO
private static final double TWO
2.- See Also:
- Constant Field Values
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CLOSE_TO_ZERO
private static final double CLOSE_TO_ZERO
The threshold for the density function where the power function base minus 1 is close to zero.- See Also:
- Constant Field Values
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mvp1Over2
private final double mvp1Over2
-(v + 1) / 2, where v = degrees of freedom.
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densityNormalisation
private final double densityNormalisation
Density normalisation factor, sqrt(v) * beta(1/2, v/2), where v = degrees of freedom.
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logDensityNormalisation
private final double logDensityNormalisation
Log density normalisation term, 0.5 * log(v) + log(beta(1/2, v/2)), where v = degrees of freedom.
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mean
private final double mean
Cached value for inverse probability function.
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variance
private final double variance
Cached value for inverse probability function.
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Method Detail
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computeVariance
static double computeVariance(double degreesOfFreedom)
- Parameters:
degreesOfFreedom
- Degrees of freedom.- Returns:
- the variance
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density
public double density(double x)
Description copied from interface:ContinuousDistribution
Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of the CDF. If the derivative does not exist atx
, then an appropriate replacement should be returned, e.g.Double.POSITIVE_INFINITY
,Double.NaN
, or the limit inferior or limit superior of the difference quotient.- Parameters:
x
- Point at which the PDF is evaluated.- Returns:
- the value of the probability density function at
x
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logDensity
public double logDensity(double x)
Description copied from interface:ContinuousDistribution
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.- Parameters:
x
- Point at which the PDF is evaluated.- Returns:
- the logarithm of the value of the probability density function
at
x
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cumulativeProbability
public double cumulativeProbability(double x)
Description copied from interface:ContinuousDistribution
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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getMean
public double getMean()
Description copied from class:TDistribution
Gets the mean of this distribution.For degrees of freedom parameter \( v \), the mean is:
\[ \mathbb{E}[X] = \begin{cases} 0 & \text{for } v \gt 1 \\ \text{undefined} & \text{otherwise} \end{cases} \]
- Specified by:
getMean
in interfaceContinuousDistribution
- Specified by:
getMean
in classTDistribution
- Returns:
- the mean, or
NaN
if it is not defined.
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getVariance
public double getVariance()
Description copied from class:TDistribution
Gets the variance of this distribution.For degrees of freedom parameter \( v \), the variance is:
\[ \operatorname{var}[X] = \begin{cases} \frac{v}{v - 2} & \text{for } v \gt 2 \\ \infty & \text{for } 1 \lt v \le 2 \\ \text{undefined} & \text{otherwise} \end{cases} \]
- Specified by:
getVariance
in interfaceContinuousDistribution
- Specified by:
getVariance
in classTDistribution
- Returns:
- the variance, or
NaN
if it is not defined.
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getMedian
double getMedian()
Description copied from class:AbstractContinuousDistribution
Gets the median. This is used to determine if the arguments to theAbstractContinuousDistribution.probability(double, double)
function are in the upper or lower domain.The default implementation calls
AbstractContinuousDistribution.inverseCumulativeProbability(double)
with a value of 0.5.- Overrides:
getMedian
in classAbstractContinuousDistribution
- Returns:
- the median
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createSampler
public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Description copied from class:AbstractContinuousDistribution
Creates a sampler.- Specified by:
createSampler
in interfaceContinuousDistribution
- Overrides:
createSampler
in classAbstractContinuousDistribution
- Parameters:
rng
- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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