Class NormalDistribution
java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.NormalDistribution
- All Implemented Interfaces:
Serializable
,RealDistribution
Implementation of the normal (gaussian) 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
ConstructorDescriptionCreate a normal distribution with mean equal to zero and standard deviation equal to one.NormalDistribution
(double mean, double sd) Create a normal distribution using the given mean, standard deviation. -
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
getMean()
Access the mean.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 standard deviation.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.double
logDensity
(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.double
probability
(double x0, double x1) For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
getSolverAbsoluteAccuracy
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Constructor Details
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NormalDistribution
public NormalDistribution()Create a normal distribution with mean equal to zero and standard deviation equal to one. -
NormalDistribution
Create a normal distribution using the given mean, standard deviation.- Parameters:
mean
- Mean for this distribution.sd
- Standard deviation for this distribution.- Throws:
MathIllegalArgumentException
- ifsd <= 0
.
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Method Details
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getMean
public double getMean()Access the mean.- Returns:
- the mean for this distribution.
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getStandardDeviation
public double getStandardDeviation()Access the standard deviation.- Returns:
- the standard deviation for 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.- 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. Ifx
is more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is withinDouble.MIN_VALUE
of 0 or 1.- 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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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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probability
For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.- Specified by:
probability
in interfaceRealDistribution
- Overrides:
probability
in classAbstractRealDistribution
- Parameters:
x0
- Lower bound (excluded).x1
- Upper bound (included).- Returns:
- the probability that a random variable with this distribution
takes a value between
x0
andx1
, excluding the lower and including the upper endpoint. - Throws:
MathIllegalArgumentException
- ifx0 > x1
. The default implementation uses the identityP(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
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getNumericalMean
public double getNumericalMean()Use this method to get the numerical value of the mean of this distribution. For mean parametermu
, the mean ismu
.- 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 standard deviation parameters
, the variance iss^2
.- 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 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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