public class TriangularDistribution extends AbstractRealDistribution
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
Constructor and Description |
---|
TriangularDistribution(double a,
double c,
double b)
Creates a triangular real distribution using the given lower limit,
upper limit, and mode.
|
TriangularDistribution(RandomGenerator rng,
double a,
double c,
double b)
Creates a triangular 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 |
getMode()
Returns the mode
c of this distribution. |
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.
|
double |
inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
|
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.
|
cumulativeProbability, logDensity, probability, probability, reseedRandomGenerator, sample, sample
public TriangularDistribution(double a, double c, double b) throws NumberIsTooLargeException, NumberIsTooSmallException
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.
a
- Lower limit of this distribution (inclusive).b
- Upper limit of this distribution (inclusive).c
- Mode of this distribution.NumberIsTooLargeException
- if a >= b
or if c > b
.NumberIsTooSmallException
- if c < a
.public TriangularDistribution(RandomGenerator rng, double a, double c, double b) throws NumberIsTooLargeException, NumberIsTooSmallException
rng
- Random number generator.a
- Lower limit of this distribution (inclusive).b
- Upper limit of this distribution (inclusive).c
- Mode of this distribution.NumberIsTooLargeException
- if a >= b
or if c > b
.NumberIsTooSmallException
- if c < a
.public double getMode()
c
of this distribution.c
of this distributionprotected double getSolverAbsoluteAccuracy()
For this distribution, the returned value is not really meaningful,
since exact formulas are implemented for the computation of the
inverseCumulativeProbability(double)
(no solver is invoked).
For lower limit a
and upper limit b
, the current
implementation returns max(ulp(a), ulp(b)
.
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
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.
For lower limit a
, upper limit b
and mode c
, the
PDF is given by
2 * (x - a) / [(b - a) * (c - a)]
if a <= x < c
,2 / (b - a)
if x = c
,2 * (b - x) / [(b - a) * (b - c)]
if c < x <= b
,0
otherwise.
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.
For lower limit a
, upper limit b
and mode c
, the
CDF is given by
0
if x < a
,(x - a)^2 / [(b - a) * (c - a)]
if a <= x < c
,(c - a) / (b - a)
if x = c
,1 - (b - x)^2 / [(b - a) * (b - c)]
if c < x <= b
,1
if x > b
.x
- the point at which the CDF is evaluatedx
public double getNumericalMean()
a
, upper limit b
, and mode c
,
the mean is (a + b + c) / 3
.Double.NaN
if it is not definedpublic double getNumericalVariance()
a
, upper limit b
, and mode c
,
the variance is (a^2 + b^2 + c^2 - a * b - a * c - b * c) / 18
.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}
.
a
of the distribution.public double getSupportUpperBound()
inverseCumulativeProbability(1)
. In other words, this
method must return
inf {x in R | P(X <= x) = 1}
.
b
of the distribution.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
public double inverseCumulativeProbability(double p) throws OutOfRangeException
X
distributed according to this distribution, the
returned value is
inf{x in R | P(X<=x) >= p}
for 0 < p <= 1
,inf{x in R | P(X<=x) > 0}
for p = 0
.RealDistribution.getSupportLowerBound()
for p = 0
,RealDistribution.getSupportUpperBound()
for p = 1
.inverseCumulativeProbability
in interface RealDistribution
inverseCumulativeProbability
in class AbstractRealDistribution
p
- the cumulative probabilityp
-quantile of this distribution
(largest 0-quantile for p = 0
)OutOfRangeException
- if p < 0
or p > 1
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