public class NormalDistribution extends AbstractRealDistribution
Modifier and Type | Field and Description |
---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
|
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.
|
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)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1) . |
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.
|
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) . |
double |
sample()
Generate a random value sampled from this distribution.
|
inverseCumulativeProbability, reseedRandomGenerator, sample
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
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()
public double getMean()
public double getStandardDeviation()
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.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 cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException
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
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()
public boolean isSupportUpperBoundInclusive()
public boolean isSupportConnected()
true
public double sample()
sample
in interface RealDistribution
sample
in class AbstractRealDistribution
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