Class TriangularDistribution
java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.TriangularDistribution
- All Implemented Interfaces:
Serializable
,RealDistribution
Implementation of the triangular real distribution.
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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
ConstructorDescriptionTriangularDistribution
(double a, double c, double b) Creates a triangular real distribution using the given lower limit, upper limit, and mode. -
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
getMode()
Returns the modec
of this distribution.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.double
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.boolean
Use this method to get information about whether the support is connected, i.e.Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
getSolverAbsoluteAccuracy, logDensity, probability
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Constructor Details
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TriangularDistribution
Creates a triangular real distribution using the given lower limit, upper limit, and mode.- Parameters:
a
- Lower limit of this distribution (inclusive).b
- Upper limit of this distribution (inclusive).c
- Mode of this distribution.- Throws:
MathIllegalArgumentException
- ifa >= b
or ifc > b
.MathIllegalArgumentException
- ifc < a
.
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Method Details
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getMode
public double getMode()Returns the modec
of this distribution.- Returns:
- the mode
c
of this distribution
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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. For lower limita
, upper limitb
and modec
, the PDF is given by2 * (x - a) / [(b - a) * (c - a)]
ifa <= x < c
,2 / (b - a)
ifx = c
,2 * (b - x) / [(b - a) * (b - c)]
ifc < x <= b
,0
otherwise.
- 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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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. For lower limita
, upper limitb
and modec
, the CDF is given by0
ifx < a
,(x - a)^2 / [(b - a) * (c - a)]
ifa <= x < c
,(c - a) / (b - a)
ifx = c
,1 - (b - x)^2 / [(b - a) * (b - c)]
ifc < x <= b
,1
ifx > b
.
- 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 lower limita
, upper limitb
, and modec
, the mean is(a + b + c) / 3
.- Returns:
- the mean or
Double.NaN
if it is not defined
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getNumericalVariance
public double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution. For lower limita
, upper limitb
, and modec
, the variance is(a^2 + b^2 + c^2 - a * b - a * c - b * c) / 18
.- Returns:
- the variance (possibly
Double.POSITIVE_INFINITY
as for certain cases inTDistribution
) orDouble.NaN
if it is not defined
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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 equal to the lower limit parameterinf {x in R | P(X <= x) > 0}
.a
of the distribution.- Returns:
- lower bound of the support
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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 equal to the upper limit parameterinf {x in R | P(X <= x) = 1}
.b
of the distribution.- Returns:
- upper bound of the support
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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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inverseCumulativeProbability
Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value isinf{x in R | P(X<=x) >= p}
for0 < p <= 1
,inf{x in R | P(X<=x) > 0}
forp = 0
.
RealDistribution.getSupportLowerBound()
forp = 0
,RealDistribution.getSupportUpperBound()
forp = 1
.
- Specified by:
inverseCumulativeProbability
in interfaceRealDistribution
- Overrides:
inverseCumulativeProbability
in classAbstractRealDistribution
- Parameters:
p
- the cumulative probability- Returns:
- the smallest
p
-quantile of this distribution (largest 0-quantile forp = 0
) - Throws:
MathIllegalArgumentException
- ifp < 0
orp > 1
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