Apache Commons Math 3.6.1 · org.apache.commons.math3.distribution.NormalDistribution

Modifier and Type	Field and Description
public static final double	DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.
private final double	logStandardDeviationPlusHalfLog2Pi The value of `log(sd) + 0.5log(2pi)` stored for faster computation.
private final double	mean Mean of this distribution.
private static final long	serialVersionUID Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID. Serializable version identifier.
private final double	solverAbsoluteAccuracy Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy. Inverse cumulative probability accuracy.
private static final double	SQRT2 √(2)
private final double	standardDeviation Standard deviation of this distribution.

Access	Constructor and Description
public	NormalDistribution() Create a normal distribution with mean equal to zero and standard deviation equal to one.
public	NormalDistribution(double Mean for this distribution. mean, double Standard deviation for this distribution. sd) Create a normal distribution using the given mean and standard deviation.
public	NormalDistribution(double Mean for this distribution. mean, double Standard deviation for this distribution. sd, double Inverse cumulative probability accuracy. inverseCumAccuracy) Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.
public	NormalDistribution(RandomGenerator Random number generator. rng, double Mean for this distribution. mean, double Standard deviation for this distribution. sd) Creates a normal distribution.
public	NormalDistribution(RandomGenerator Random number generator. rng, double Mean for this distribution. mean, double Standard deviation for this distribution. sd, double Inverse cumulative probability accuracy. inverseCumAccuracy) Creates a normal distribution.

Method Summary

Modifier and Type	Method and Description
public double	cumulativeProbability(double the point at which the CDF is evaluated x) Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
public double	cumulativeProbability(double the exclusive lower bound x0, double the inclusive upper bound x1) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.cumulativeProbability. Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. Deprecated See `RealDistribution#cumulativeProbability(double, double)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.
public double	density(double the point at which the PDF is evaluated x) Implements org.apache.commons.math3.distribution.RealDistribution.density. Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
public double	Returns: the mean for this distribution. getMean() Access the mean.
public double	getNumericalMean() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean. Use this method to get the numerical value of the mean of this distribution.
public double	getNumericalVariance() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance. Use this method to get the numerical value of the variance of this distribution.
protected double	getSolverAbsoluteAccuracy() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy. Returns the solver absolute accuracy for inverse cumulative computation.
public double	Returns: the standard deviation for this distribution. getStandardDeviation() Access the standard deviation.
public double	Returns: lower bound of the support (always `Double.NEGATIVE_INFINITY`) getSupportLowerBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound. Access the lower bound of the support.
public double	Returns: upper bound of the support (always `Double.POSITIVE_INFINITY`) getSupportUpperBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound. Access the upper bound of the support.
public double	inverseCumulativeProbability(final double the cumulative probability p) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability. Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability. Computes the quantile function of this distribution.
public boolean	Returns: `true` isSupportConnected() Implements org.apache.commons.math3.distribution.RealDistribution.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.
public boolean	isSupportLowerBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive. Whether or not the lower bound of support is in the domain of the density function.
public boolean	isSupportUpperBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive. Whether or not the upper bound of support is in the domain of the density function.
public double	logDensity(double the point at which the PDF is evaluated x) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity. Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point `x`.
public double	probability(double Lower bound (excluded). x0, double Upper bound (included). x1) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.probability. For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.
public double	sample() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.sample. Implements org.apache.commons.math3.distribution.RealDistribution.sample. Generate a random value sampled from this distribution.

Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:: probability reseedRandomGenerator sample

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY	back to summary
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy. Since 2.1

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

back to summary

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since: 2.1

logStandardDeviationPlusHalfLog2Pi	back to summary
private final double logStandardDeviationPlusHalfLog2Pi The value of `log(sd) + 0.5log(2pi)` stored for faster computation.

mean	back to summary
private final double mean Mean of this distribution.

serialVersionUID	back to summary
private static final long serialVersionUID Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID. Serializable version identifier.

serialVersionUID

back to summary

private static final long serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.

solverAbsoluteAccuracy	back to summary
private final double solverAbsoluteAccuracy Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy. Inverse cumulative probability accuracy.

solverAbsoluteAccuracy

back to summary

private final double solverAbsoluteAccuracy

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy.

Inverse cumulative probability accuracy.

SQRT2	back to summary
private static final double SQRT2 √(2)

standardDeviation	back to summary
private final double standardDeviation Standard deviation of this distribution.

Constructor Detail

NormalDistribution back to summary

NormalDistribution	back to summary
public NormalDistribution() Create a normal distribution with mean equal to zero and standard deviation equal to one. Note this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `sample(int)`). In case no sampling is needed for the created distribution, it is advised to pass `null` as random generator via the appropriate constructors to avoid the additional initialisation overhead.

public NormalDistribution()

Create a normal distribution with mean equal to zero and standard deviation equal to one.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

NormalDistribution back to summary

NormalDistribution	back to summary
public NormalDistribution(double mean, double sd) throws NotStrictlyPositiveException Create a normal distribution using the given mean and standard deviation. Note this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `sample(int)`). In case no sampling is needed for the created distribution, it is advised to pass `null` as random generator via the appropriate constructors to avoid the additional initialisation overhead. Parameters mean:double Mean for this distribution. sd:double Standard deviation for this distribution. Exceptions NotStrictlyPositiveException: if `sd <= 0`.

public NormalDistribution(double mean, double sd) throws NotStrictlyPositiveException

Create a normal distribution using the given mean and standard deviation.

Note

Parameters

mean:double: Mean for this distribution.
sd:double: Standard deviation for this distribution.

Exceptions

NotStrictlyPositiveException:: if sd <= 0.

NormalDistribution back to summary

NormalDistribution	back to summary
public NormalDistribution(double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy. Note this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `sample(int)`). In case no sampling is needed for the created distribution, it is advised to pass `null` as random generator via the appropriate constructors to avoid the additional initialisation overhead. Parameters mean:double Mean for this distribution. sd:double Standard deviation for this distribution. inverseCumAccuracy:double Inverse cumulative probability accuracy. Exceptions NotStrictlyPositiveException: if `sd <= 0`. Since 2.1

public NormalDistribution(double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException

Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.

Note

Parameters

mean:double: Mean for this distribution.
sd:double: Standard deviation for this distribution.
inverseCumAccuracy:double: Inverse cumulative probability accuracy.

Exceptions

NotStrictlyPositiveException:: if sd <= 0.

Since

2.1

NormalDistribution back to summary

NormalDistribution	back to summary
public NormalDistribution(RandomGenerator rng, double mean, double sd) throws NotStrictlyPositiveException Creates a normal distribution. Parameters rng:RandomGenerator Random number generator. mean:double Mean for this distribution. sd:double Standard deviation for this distribution. Exceptions NotStrictlyPositiveException: if `sd <= 0`. Since 3.3

public NormalDistribution(RandomGenerator rng, double mean, double sd) throws NotStrictlyPositiveException

Creates a normal distribution.

Parameters

rng:RandomGenerator: Random number generator.
mean:double: Mean for this distribution.
sd:double: Standard deviation for this distribution.

Exceptions

NotStrictlyPositiveException:: if sd <= 0.

Since

3.3

NormalDistribution back to summary

NormalDistribution	back to summary
public NormalDistribution(RandomGenerator rng, double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException Creates a normal distribution. Parameters rng:RandomGenerator Random number generator. mean:double Mean for this distribution. sd:double Standard deviation for this distribution. inverseCumAccuracy:double Inverse cumulative probability accuracy. Exceptions NotStrictlyPositiveException: if `sd <= 0`. Since 3.1

public NormalDistribution(RandomGenerator rng, double mean, double sd, double inverseCumAccuracy) throws NotStrictlyPositiveException

Creates a normal distribution.

Parameters

rng:RandomGenerator: Random number generator.
mean:double: Mean for this distribution.
sd:double: Standard deviation for this distribution.
inverseCumAccuracy:double: Inverse cumulative probability accuracy.

Exceptions

NotStrictlyPositiveException:: if sd <= 0.

Since

3.1

Method Detail

cumulativeProbability back to summary

cumulativeProbability	back to summary
public double cumulativeProbability(double x) Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. For a random variable `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. Parameters x:double the point at which the CDF is evaluated Returns:double the probability that a random variable with this distribution takes a value less than or equal to `x`

public double cumulativeProbability(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

For a random variable 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.

Parameters

x:double: the point at which the CDF is evaluated

Returns:double

the probability that a random variable with this distribution takes a value less than or equal to x

cumulativeProbability back to summary

cumulativeProbability	back to summary
public double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.cumulativeProbability. Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.cumulativeProbability. Deprecated See `RealDistribution#cumulativeProbability(double, double)` For a random variable `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)` Parameters x0:double Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. the exclusive lower bound x1:double Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. the inclusive upper bound Returns:double Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. the probability that a random variable with this distribution takes a value between `x0` and `x1`, excluding the lower and including the upper endpoint Annotations @Override @Deprecated Exceptions NumberIsTooLargeException: Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. if `x0 > x1`

public double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.cumulativeProbability.

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.cumulativeProbability.

Deprecated

See RealDistribution#cumulativeProbability(double, double)

For a random variable 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)

Parameters

x0:double

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

the exclusive lower bound

x1:double

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

the inclusive upper bound

Returns:double

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint

Annotations

@Override
@Deprecated

Exceptions

NumberIsTooLargeException:

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

if x0 > x1

density back to summary

density	back to summary
public double density(double x) Implements org.apache.commons.math3.distribution.RealDistribution.density. Doc from org.apache.commons.math3.distribution.RealDistribution.density. Returns the probability density function (PDF) of this distribution evaluated at the specified point `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. Parameters x:double the point at which the PDF is evaluated Returns:double the value of the probability density function at point `x`

public double density(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Doc from org.apache.commons.math3.distribution.RealDistribution.density.

Returns the probability density function (PDF) of this distribution evaluated at the specified point 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.

Parameters

x:double: the point at which the PDF is evaluated

Returns:double

the value of the probability density function at point x

getMean	back to summary
public double getMean() Access the mean. Returns:double the mean for this distribution.

getMean

back to summary

public double getMean()

Access the mean.

Returns:double: the mean for this distribution.

getNumericalMean back to summary

getNumericalMean	back to summary
public double getNumericalMean() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean. Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalMean. Use this method to get the numerical value of the mean of this distribution. For mean parameter `mu`, the mean is `mu`. Returns:double the mean or `Double.NaN` if it is not defined

public double getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Use this method to get the numerical value of the mean of this distribution. For mean parameter mu, the mean is mu.

Returns:double: the mean or Double.NaN if it is not defined

getNumericalVariance back to summary

getNumericalVariance	back to summary
public double getNumericalVariance() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance. Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance. Use this method to get the numerical value of the variance of this distribution. For standard deviation parameter `s`, the variance is `s^2`. Returns:double the variance (possibly `Double.POSITIVE_INFINITY` as for certain cases in `TDistribution`) or `Double.NaN` if it is not defined

public double getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Use this method to get the numerical value of the variance of this distribution. For standard deviation parameter s, the variance is s^2.

Returns:double: the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSolverAbsoluteAccuracy	back to summary
protected double getSolverAbsoluteAccuracy() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy. Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default. Returns:double the maximum absolute error in inverse cumulative probability estimates Annotations @Override

getSolverAbsoluteAccuracy

back to summary

protected double getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Returns:double

the maximum absolute error in inverse cumulative probability estimates

Annotations

@Override

getStandardDeviation	back to summary
public double getStandardDeviation() Access the standard deviation. Returns:double the standard deviation for this distribution.

getStandardDeviation

back to summary

public double getStandardDeviation()

Access the standard deviation.

Returns:double: the standard deviation for this distribution.

getSupportLowerBound back to summary

getSupportLowerBound	back to summary
public double getSupportLowerBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound. Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound. Access the lower bound of the support. This method must return the same value as `inverseCumulativeProbability(0)`. In other words, this method must return `inf {x in R \| P(X <= x) > 0}`. The lower bound of the support is always negative infinity no matter the parameters. Returns:double lower bound of the support (always `Double.NEGATIVE_INFINITY`)

public double getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always negative infinity no matter the parameters.

Returns:double: lower bound of the support (always Double.NEGATIVE_INFINITY)

getSupportUpperBound back to summary

getSupportUpperBound	back to summary
public double getSupportUpperBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound. Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound. Access the upper bound of the support. This method must return the same value as `inverseCumulativeProbability(1)`. In other words, this method must return `inf {x in R \| P(X <= x) = 1}`. The upper bound of the support is always positive infinity no matter the parameters. Returns:double upper bound of the support (always `Double.POSITIVE_INFINITY`)

public double getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:double: upper bound of the support (always Double.POSITIVE_INFINITY)

inverseCumulativeProbability back to summary

inverseCumulativeProbability	back to summary
public double inverseCumulativeProbability(final double p) throws OutOfRangeException Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability. Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability. Computes the quantile function of this distribution. For a random variable `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`. The default implementation returns `getSupportLowerBound()` for `p = 0`, `getSupportUpperBound()` for `p = 1`. Parameters p:double Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability. the cumulative probability Returns:double Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability. the smallest `p`-quantile of this distribution (largest 0-quantile for `p = 0`) Annotations @Override Exceptions OutOfRangeException: Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability. if `p < 0` or `p > 1` Since 3.2

public double inverseCumulativeProbability(final double p) throws OutOfRangeException

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

Computes the quantile function of this distribution. For a random variable 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.

The default implementation returns

getSupportLowerBound() for p = 0,
getSupportUpperBound() for p = 1.

Parameters

p:double

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

the cumulative probability

Returns:double

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

the smallest p-quantile of this distribution (largest 0-quantile for p = 0)

Annotations

@Override

Exceptions

OutOfRangeException:

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

if p < 0 or p > 1

Since

3.2

isSupportConnected back to summary

isSupportConnected	back to summary
public boolean isSupportConnected() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected. Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean `true`

public boolean isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean: true

isSupportLowerBoundInclusive back to summary

isSupportLowerBoundInclusive	back to summary
public boolean isSupportLowerBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive. Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive. Whether or not the lower bound of support is in the domain of the density function. Returns true iff `getSupporLowerBound()` is finite and `density(getSupportLowerBound())` returns a non-NaN, non-infinite value. Returns:boolean true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

public boolean isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:boolean: true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive back to summary

isSupportUpperBoundInclusive	back to summary
public boolean isSupportUpperBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive. Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive. Whether or not the upper bound of support is in the domain of the density function. Returns true iff `getSupportUpperBound()` is finite and `density(getSupportUpperBound())` returns a non-NaN, non-infinite value. Returns:boolean true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

public boolean isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:boolean: true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

logDensity back to summary

logDensity	back to summary
public double logDensity(double x) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity. Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point `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 `density(double)`. The default implementation simply computes the logarithm of `density(x)`. Parameters x:double the point at which the PDF is evaluated Returns:double the logarithm of the value of the probability density function at point `x` Annotations @Override

public double logDensity(double x)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point 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 density(double). The default implementation simply computes the logarithm of density(x).

Parameters

x:double: the point at which the PDF is evaluated

Returns:double

the logarithm of the value of the probability density function at point x

Annotations

@Override

probability back to summary

probability	back to summary
public double probability(double x0, double x1) throws NumberIsTooLargeException Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.probability. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.probability. For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`. Parameters x0:double Lower bound (excluded). x1:double Upper bound (included). Returns:double the probability that a random variable with this distribution takes a value between `x0` and `x1`, excluding the lower and including the upper endpoint. Annotations @Override Exceptions NumberIsTooLargeException: if `x0 > x1`. The default implementation uses the identity `P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)`

public double probability(double x0, double x1) throws NumberIsTooLargeException

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.probability.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.probability.

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Parameters

x0:double: Lower bound (excluded).
x1:double: Upper bound (included).

Returns:double

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

Annotations

@Override

Exceptions

NumberIsTooLargeException:: if x0 > x1. The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

sample	back to summary
public double sample() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.sample. Implements org.apache.commons.math3.distribution.RealDistribution.sample. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.sample. Generate a random value sampled from this distribution. The default implementation uses the inversion method. Returns:double Doc from org.apache.commons.math3.distribution.RealDistribution.sample. a random value. Annotations @Override

sample

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public double sample()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.sample.

Implements org.apache.commons.math3.distribution.RealDistribution.sample.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.sample.

Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Returns:double

Doc from org.apache.commons.math3.distribution.RealDistribution.sample.

a random value.

Annotations

@Override

public Class NormalDistribution

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