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

Modifier and Type	Field and Description
public static final double	DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.
private final double	scale The scale parameter of this distribution.
private static final long	serialVersionUID Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID. Serializable version identifier.
private final double	shape The shape parameter of this distribution.
private final double	solverAbsoluteAccuracy Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy. Inverse cumulative probability accuracy.

Access	Constructor and Description
public	ParetoDistribution() Create a Pareto distribution with a scale of `1` and a shape of `1`.
public	ParetoDistribution(double the scale parameter of this distribution scale, double the shape parameter of this distribution shape) Create a Pareto distribution using the specified scale and shape.
public	ParetoDistribution(double the scale parameter of this distribution scale, double the shape parameter of this distribution shape, double Inverse cumulative probability accuracy. inverseCumAccuracy) Create a Pareto distribution using the specified scale, shape and inverse cumulative distribution accuracy.
public	ParetoDistribution(RandomGenerator Random number generator. rng, double Scale parameter of this distribution. scale, double Shape parameter of this distribution. shape) Creates a Pareto distribution.
public	ParetoDistribution(RandomGenerator Random number generator. rng, double Scale parameter of this distribution. scale, double Shape parameter of this distribution. shape, double Inverse cumulative probability accuracy. inverseCumAccuracy) Creates a Pareto 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	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.
public double	Returns: the scale parameter getScale() Returns the scale parameter of this distribution.
public double	Returns: the shape parameter getShape() Returns the shape parameter 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: lower bound of the support 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 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	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:: inverseCumulativeProbability probability 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.

scale	back to summary
private final double scale The scale parameter 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.

shape	back to summary
private final double shape The shape parameter of this distribution.

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.

Constructor Detail

ParetoDistribution	back to summary
public ParetoDistribution() Create a Pareto distribution with a scale of `1` and a shape of `1`.

ParetoDistribution back to summary

ParetoDistribution	back to summary
public ParetoDistribution(double scale, double shape) throws NotStrictlyPositiveException Create a Pareto distribution using the specified scale and shape. 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 scale:double the scale parameter of this distribution shape:double the shape parameter of this distribution Exceptions NotStrictlyPositiveException: if `scale <= 0` or `shape <= 0`.

public ParetoDistribution(double scale, double shape) throws NotStrictlyPositiveException

Create a Pareto distribution using the specified scale and shape.

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

scale:double: the scale parameter of this distribution
shape:double: the shape parameter of this distribution

Exceptions

NotStrictlyPositiveException:: if scale <= 0 or shape <= 0.

ParetoDistribution back to summary

ParetoDistribution	back to summary
public ParetoDistribution(double scale, double shape, double inverseCumAccuracy) throws NotStrictlyPositiveException Create a Pareto distribution using the specified scale, shape 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 scale:double the scale parameter of this distribution shape:double the shape parameter of this distribution inverseCumAccuracy:double Inverse cumulative probability accuracy. Exceptions NotStrictlyPositiveException: if `scale <= 0` or `shape <= 0`.

public ParetoDistribution(double scale, double shape, double inverseCumAccuracy) throws NotStrictlyPositiveException

Create a Pareto distribution using the specified scale, shape and inverse cumulative distribution accuracy.

Note

Parameters

scale:double: the scale parameter of this distribution
shape:double: the shape parameter of this distribution
inverseCumAccuracy:double: Inverse cumulative probability accuracy.

Exceptions

NotStrictlyPositiveException:: if scale <= 0 or shape <= 0.

ParetoDistribution back to summary

ParetoDistribution	back to summary
public ParetoDistribution(RandomGenerator rng, double scale, double shape) throws NotStrictlyPositiveException Creates a Pareto distribution. Parameters rng:RandomGenerator Random number generator. scale:double Scale parameter of this distribution. shape:double Shape parameter of this distribution. Exceptions NotStrictlyPositiveException: if `scale <= 0` or `shape <= 0`.

public ParetoDistribution(RandomGenerator rng, double scale, double shape) throws NotStrictlyPositiveException

Creates a Pareto distribution.

Parameters

rng:RandomGenerator: Random number generator.
scale:double: Scale parameter of this distribution.
shape:double: Shape parameter of this distribution.

Exceptions

NotStrictlyPositiveException:: if scale <= 0 or shape <= 0.

ParetoDistribution back to summary

ParetoDistribution	back to summary
public ParetoDistribution(RandomGenerator rng, double scale, double shape, double inverseCumAccuracy) throws NotStrictlyPositiveException Creates a Pareto distribution. Parameters rng:RandomGenerator Random number generator. scale:double Scale parameter of this distribution. shape:double Shape parameter of this distribution. inverseCumAccuracy:double Inverse cumulative probability accuracy. Exceptions NotStrictlyPositiveException: if `scale <= 0` or `shape <= 0`.

public ParetoDistribution(RandomGenerator rng, double scale, double shape, double inverseCumAccuracy) throws NotStrictlyPositiveException

Creates a Pareto distribution.

Parameters

rng:RandomGenerator: Random number generator.
scale:double: Scale parameter of this distribution.
shape:double: Shape parameter of this distribution.
inverseCumAccuracy:double: Inverse cumulative probability accuracy.

Exceptions

NotStrictlyPositiveException:: if scale <= 0 or shape <= 0.

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. For scale `k`, and shape `α` of this distribution, the CDF is given by `0` if `x < k`, `1 - (k / x)^α` otherwise. 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.

For scale k, and shape α of this distribution, the CDF is given by

0 if x < k,
1 - (k / x)^α otherwise.

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. For scale `k`, and shape `α` of this distribution, the PDF is given by `0` if `x < k`, `α * k^α / x^(α + 1)` otherwise. 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.

For scale k, and shape α of this distribution, the PDF is given by

0 if x < k,
α * k^α / x^(α + 1) otherwise.

Parameters

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

Returns:double

the value of the probability density function at point x

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 scale `k` and shape `α`, the mean is given by `∞` if `α <= 1`, `α * k / (α - 1)` otherwise. 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 scale k and shape α, the mean is given by

∞ if α <= 1,
α * k / (α - 1) otherwise.

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 scale `k` and shape `α`, the variance is given by `∞` if `1 < α <= 2`, `k^2 * α / ((α - 1)^2 * (α - 2))` otherwise. 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 scale k and shape α, the variance is given by

∞ if 1 < α <= 2,
k^2 * α / ((α - 1)^2 * (α - 2)) otherwise.

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

getScale	back to summary
public double getScale() Returns the scale parameter of this distribution. Returns:double the scale parameter

getScale

back to summary

public double getScale()

Returns the scale parameter of this distribution.

Returns:double: the scale parameter

getShape	back to summary
public double getShape() Returns the shape parameter of this distribution. Returns:double the shape parameter

getShape

back to summary

public double getShape()

Returns the shape parameter of this distribution.

Returns:double: the shape parameter

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

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 equal to the scale parameter `k`. Returns:double lower bound of the support

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 equal to the scale parameter k.

Returns:double: lower bound of the support

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)

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)`. See documentation of `density(double)` for computation details. 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). See documentation of density(double) for computation details.

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

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

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

public Class ParetoDistribution

Field Summary

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Method Detail