public class NormalDistribution 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 |
---|
NormalDistribution()
Create 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 and standard deviation.
|
NormalDistribution(double mean,
double sd,
double inverseCumAccuracy)
Create a normal distribution using the given mean, standard deviation and
inverse cumulative distribution accuracy.
|
NormalDistribution(RandomGenerator rng,
double mean,
double sd)
Creates a normal distribution.
|
NormalDistribution(RandomGenerator rng,
double mean,
double sd,
double inverseCumAccuracy)
Creates a normal 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 |
cumulativeProbability(double x0,
double x1)
Deprecated.
|
double |
density(double x)
Returns the probability density function (PDF) of this distribution
evaluated at the specified point
x . |
double |
getMean()
Access the mean.
|
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 |
getStandardDeviation()
Access the standard deviation.
|
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.
|
double |
logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution
evaluated at the specified point
x . |
double |
probability(double x0,
double x1)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1) . |
double |
sample()
Generate a random value sampled from this distribution.
|
probability, reseedRandomGenerator, sample
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
public NormalDistribution()
public NormalDistribution(double mean, double sd) throws NotStrictlyPositiveException
mean
- Mean for this distribution.sd
- Standard deviation for this distribution.NotStrictlyPositiveException
- if sd <= 0
.public NormalDistribution(double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException
mean
- Mean for this distribution.sd
- Standard deviation for this distribution.inverseCumAccuracy
- Inverse cumulative probability accuracy.NotStrictlyPositiveException
- if sd <= 0
.public NormalDistribution(RandomGenerator rng, double mean, double sd) throws NotStrictlyPositiveException
rng
- Random number generator.mean
- Mean for this distribution.sd
- Standard deviation for this distribution.NotStrictlyPositiveException
- if sd <= 0
.public NormalDistribution(RandomGenerator rng, double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException
rng
- Random number generator.mean
- Mean for this distribution.sd
- Standard deviation for this distribution.inverseCumAccuracy
- Inverse cumulative probability accuracy.NotStrictlyPositiveException
- if sd <= 0
.public double getMean()
public double getStandardDeviation()
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.
If x
is more than 40 standard deviations from the mean, 0 or 1
is returned, as in these cases the actual value is within
Double.MIN_VALUE
of 0 or 1.x
- the point at which the CDF is evaluatedx
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
@Deprecated public double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException
RealDistribution.cumulativeProbability(double,double)
X
whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1)
.
The default implementation uses the identity
P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
cumulativeProbability
in interface RealDistribution
cumulativeProbability
in class AbstractRealDistribution
x0
- the exclusive lower boundx1
- the inclusive upper boundx0
and x1
,
excluding the lower and including the upper endpointNumberIsTooLargeException
- if x0 > x1
public double probability(double x0, double x1) throws NumberIsTooLargeException
X
whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1)
.probability
in class AbstractRealDistribution
x0
- Lower bound (excluded).x1
- Upper bound (included).x0
and x1
, excluding the lower
and including the upper endpoint.NumberIsTooLargeException
- if x0 > x1
.
The default implementation uses the identity
P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
public double getNumericalMean()
mu
, the mean is mu
.Double.NaN
if it is not definedpublic double getNumericalVariance()
s
, the variance is s^2
.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
public double sample()
sample
in interface RealDistribution
sample
in class AbstractRealDistribution
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