Class TDistribution
java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.TDistribution
- All Implemented Interfaces:
Serializable
,RealDistribution
Implementation of Student's t-distribution.
- See Also:
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Field Summary
Fields inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
DEFAULT_SOLVER_ABSOLUTE_ACCURACY
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Constructor Summary
ConstructorDescriptionTDistribution
(double degreesOfFreedom) Create a t distribution using the given degrees of freedom.TDistribution
(double degreesOfFreedom, double inverseCumAccuracy) Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy. -
Method Summary
Modifier and TypeMethodDescriptiondouble
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
Access the degrees of freedom.double
Use this method to get the numerical value of the mean of this distribution.double
Use this method to get the numerical value of the variance of this distribution.double
Access the lower bound of the support.double
Access the upper bound of the support.boolean
Use this method to get information about whether the support is connected, i.e.double
logDensity
(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
getSolverAbsoluteAccuracy, inverseCumulativeProbability, probability
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Constructor Details
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TDistribution
Create a t distribution using the given degrees of freedom.- Parameters:
degreesOfFreedom
- Degrees of freedom.- Throws:
MathIllegalArgumentException
- ifdegreesOfFreedom <= 0
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TDistribution
public TDistribution(double degreesOfFreedom, double inverseCumAccuracy) throws MathIllegalArgumentException Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.- Parameters:
degreesOfFreedom
- Degrees of freedom.inverseCumAccuracy
- the maximum absolute error in inverse cumulative probability estimates (defaults toAbstractRealDistribution.DEFAULT_SOLVER_ABSOLUTE_ACCURACY
).- Throws:
MathIllegalArgumentException
- ifdegreesOfFreedom <= 0
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Method Details
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getDegreesOfFreedom
public double getDegreesOfFreedom()Access the degrees of freedom.- Returns:
- the degrees of freedom.
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density
public double density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. 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
- the point at which the PDF is evaluated- Returns:
- the value of the probability density function at point
x
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logDensity
public double logDensity(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. 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. 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 ofRealDistribution.density(double)
.The default implementation simply computes the logarithm of
density(x)
.- Specified by:
logDensity
in interfaceRealDistribution
- Overrides:
logDensity
in classAbstractRealDistribution
- Parameters:
x
- the point at which the PDF is evaluated- Returns:
- the logarithm of the value of the probability density function at point
x
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cumulativeProbability
public double cumulativeProbability(double 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
- the 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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getNumericalMean
public double getNumericalMean()Use this method to get the numerical value of the mean of this distribution. For degrees of freedom parameterdf
, the mean is- if
df > 1
then0
, - else undefined (
Double.NaN
).
- Returns:
- the mean or
Double.NaN
if it is not defined
- if
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getNumericalVariance
public double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution. For degrees of freedom parameterdf
, the variance is- if
df > 2
thendf / (df - 2)
, - if
1 < df <= 2
then positive infinity (Double.POSITIVE_INFINITY
), - else undefined (
Double.NaN
).
- Returns:
- the variance (possibly
Double.POSITIVE_INFINITY
as for certain cases inTDistribution
) orDouble.NaN
if it is not defined
- if
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getSupportLowerBound
public double getSupportLowerBound()Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must return
The lower bound of the support is always negative infinity no matter the parameters.inf {x in R | P(X <= x) > 0}
.- Returns:
- lower bound of the support (always
Double.NEGATIVE_INFINITY
)
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getSupportUpperBound
public double getSupportUpperBound()Access the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
. In other words, this method must return
The upper bound of the support is always positive infinity no matter the parameters.inf {x in R | P(X <= x) = 1}
.- Returns:
- upper bound of the support (always
Double.POSITIVE_INFINITY
)
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isSupportConnected
public boolean isSupportConnected()Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.- Returns:
true
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