public class TriangularDistribution extends AbstractRealDistribution
randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
Constructor and Description |
---|
TriangularDistribution(double a,
double c,
double b)
Create a triangular real distribution using the given lower limit,
upper limit, and mode.
|
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()
Use this method to get information about whether the lower bound
of the support is inclusive or not.
|
boolean |
isSupportUpperBoundInclusive()
Use this method to get information about whether the upper bound
of the support is inclusive or not.
|
double |
probability(double x)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(X = x) . |
cumulativeProbability, reseedRandomGenerator, sample, sample
public TriangularDistribution(double a, double c, double b) throws NumberIsTooLargeException, NumberIsTooSmallException
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 probability(double x)
X
whose values are distributed according
to this distribution, this method returns P(X = x)
. In other
words, this method represents the probability mass function (PMF)
for the distribution.
For this distribution P(X = x)
always evaluates to 0.x
- the point at which the PMF is evaluatedpublic 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()
public boolean isSupportUpperBoundInclusive()
public boolean isSupportConnected()
true
public double inverseCumulativeProbability(double p) throws OutOfRangeException
AbstractRealDistribution
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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