public class TDistribution extends AbstractRealDistribution
Modifier and Type | Field and Description |
---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
|
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
Constructor and Description |
---|
TDistribution(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.
|
TDistribution(RandomGenerator rng,
double degreesOfFreedom)
Creates a t distribution.
|
TDistribution(RandomGenerator rng,
double degreesOfFreedom,
double inverseCumAccuracy)
Creates a t distribution.
|
Modifier and Type | Method and Description |
---|---|
double |
cumulativeProbability(double x)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(X <= x) . |
double |
density(double x)
Returns the probability density function (PDF) of this distribution
evaluated at the specified point
x . |
double |
getDegreesOfFreedom()
Access the degrees of freedom.
|
double |
getNumericalMean()
Use this method to get the numerical value of the mean of this
distribution.
|
double |
getNumericalVariance()
Use this method to get the numerical value of the variance of this
distribution.
|
protected double |
getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation.
|
double |
getSupportLowerBound()
Access the lower bound of the support.
|
double |
getSupportUpperBound()
Access the upper bound of the support.
|
boolean |
isSupportConnected()
Use this method to get information about whether the support is connected,
i.e.
|
boolean |
isSupportLowerBoundInclusive()
Whether or not the lower bound of support is in the domain of the density
function.
|
boolean |
isSupportUpperBoundInclusive()
Whether or not the upper bound of support is in the domain of the density
function.
|
double |
logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution
evaluated at the specified point
x . |
cumulativeProbability, inverseCumulativeProbability, probability, probability, reseedRandomGenerator, sample, sample
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
public TDistribution(double degreesOfFreedom) throws NotStrictlyPositiveException
Note: this constructor will implicitly create an instance of
Well19937c
as random generator to be used for sampling only (see
AbstractRealDistribution.sample()
and AbstractRealDistribution.sample(int)
). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
degreesOfFreedom
- Degrees of freedom.NotStrictlyPositiveException
- if degreesOfFreedom <= 0
public TDistribution(double degreesOfFreedom, double inverseCumAccuracy) throws NotStrictlyPositiveException
Note: this constructor will implicitly create an instance of
Well19937c
as random generator to be used for sampling only (see
AbstractRealDistribution.sample()
and AbstractRealDistribution.sample(int)
). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
degreesOfFreedom
- Degrees of freedom.inverseCumAccuracy
- the maximum absolute error in inverse
cumulative probability estimates
(defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).NotStrictlyPositiveException
- if degreesOfFreedom <= 0
public TDistribution(RandomGenerator rng, double degreesOfFreedom) throws NotStrictlyPositiveException
rng
- Random number generator.degreesOfFreedom
- Degrees of freedom.NotStrictlyPositiveException
- if degreesOfFreedom <= 0
public TDistribution(RandomGenerator rng, double degreesOfFreedom, double inverseCumAccuracy) throws NotStrictlyPositiveException
rng
- Random number generator.degreesOfFreedom
- Degrees of freedom.inverseCumAccuracy
- the maximum absolute error in inverse
cumulative probability estimates
(defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).NotStrictlyPositiveException
- if degreesOfFreedom <= 0
public double getDegreesOfFreedom()
public double density(double x)
x
. In general, the PDF is
the derivative of the CDF
.
If the derivative does not exist at x
, 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.x
- the point at which the PDF is evaluatedx
public double logDensity(double x)
x
. In general, the PDF is the derivative of the
CDF
. If the derivative does not exist at x
,
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 of
RealDistribution.density(double)
. The default implementation simply computes the logarithm of
density(x)
.logDensity
in class AbstractRealDistribution
x
- the point at which the PDF is evaluatedx
public double cumulativeProbability(double x)
X
whose values are distributed according
to this distribution, this method returns P(X <= x)
. In other
words, this method represents the (cumulative) distribution function
(CDF) for this distribution.x
- the point at which the CDF is evaluatedx
protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
public double getNumericalMean()
df
, the mean is
df > 1
then 0
,Double.NaN
).Double.NaN
if it is not definedpublic double getNumericalVariance()
df
, the variance is
df > 2
then df / (df - 2)
,1 < df <= 2
then positive infinity
(Double.POSITIVE_INFINITY
),Double.NaN
).Double.POSITIVE_INFINITY
as
for certain cases in TDistribution
) or Double.NaN
if it
is not definedpublic double getSupportLowerBound()
inverseCumulativeProbability(0)
. In other words, this
method must return
inf {x in R | P(X <= x) > 0}
.
Double.NEGATIVE_INFINITY
)public double getSupportUpperBound()
inverseCumulativeProbability(1)
. In other words, this
method must return
inf {x in R | P(X <= x) = 1}
.
Double.POSITIVE_INFINITY
)public boolean isSupportLowerBoundInclusive()
getSupporLowerBound()
is finite and
density(getSupportLowerBound())
returns a non-NaN, non-infinite
value.public boolean isSupportUpperBoundInclusive()
getSupportUpperBound()
is finite and
density(getSupportUpperBound())
returns a non-NaN, non-infinite
value.public boolean isSupportConnected()
true
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