gov.sandia.cognition.statistics.distribution
Class UnivariateGaussian.CDF

java.lang.Object
  gov.sandia.cognition.util.AbstractCloneableSerializable
      gov.sandia.cognition.statistics.AbstractDistribution<NumberType>
          gov.sandia.cognition.statistics.AbstractClosedFormUnivariateDistribution<Double>
              gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution
                  gov.sandia.cognition.statistics.distribution.UnivariateGaussian
                      gov.sandia.cognition.statistics.distribution.UnivariateGaussian.CDF

All Implemented Interfaces:

Evaluator<Double,Double>, ClosedFormDifferentiableEvaluator<Double,Double,Double>, DifferentiableEvaluator<Double,Double,Double>, Vectorizable, ScalarFunction<Double>, UnivariateScalarFunction, ClosedFormComputableDistribution<Double>, ClosedFormCumulativeDistributionFunction<Double>, ClosedFormDistribution<Double>, ClosedFormUnivariateDistribution<Double>, ComputableDistribution<Double>, CumulativeDistributionFunction<Double>, Distribution<Double>, DistributionWithMean<Double>, EstimableDistribution<Double,UnivariateGaussian>, InvertibleCumulativeDistributionFunction<Double>, SmoothCumulativeDistributionFunction, SmoothUnivariateDistribution, UnivariateDistribution<Double>, CloneableSerializable, Serializable, Cloneable

Enclosing class:

UnivariateGaussian

public static class UnivariateGaussian.CDF
extends UnivariateGaussian
implements SmoothCumulativeDistributionFunction, InvertibleCumulativeDistributionFunction<Double>

CDF of the underlying Gaussian.

See Also:

Serialized Form

Nested Class Summary

static class

UnivariateGaussian.CDF.Inverse Inverts the CumulativeDistribution function.

Nested classes/interfaces inherited from class gov.sandia.cognition.statistics.distribution.UnivariateGaussian

UnivariateGaussian.CDF, UnivariateGaussian.ErrorFunction, UnivariateGaussian.IncrementalEstimator, UnivariateGaussian.MaximumLikelihoodEstimator, UnivariateGaussian.PDF, UnivariateGaussian.SufficientStatistic, UnivariateGaussian.WeightedMaximumLikelihoodEstimator

Field Summary

Fields inherited from class gov.sandia.cognition.statistics.distribution.UnivariateGaussian

BIG_Z, DEFAULT_MEAN, DEFAULT_VARIANCE, mean, PI2, SQRT2, variance

Constructor Summary

UnivariateGaussian.CDF()
Creates a new instance of UnivariateGaussian with zero mean and unit variance

UnivariateGaussian.CDF(double mean, double variance)
Creates a new instance of UnivariateGaussian

UnivariateGaussian.CDF(UnivariateGaussian other)
Copy constructor

Method Summary

Double	differentiate(Double input) Differentiates the output with respect to the input
double	evaluate(double z) Produces a double output for the given double input
Double	evaluate(Double input) Evaluates the function on the given input and returns the output.
static double	evaluate(double z, double mean, double variance) Computes the cumulative distribution of a Normalized Gaussian distribution using the errorFunction method.
double	evaluateAsDouble(Double input) Evaluates the scalar function as a double.
UnivariateGaussian.CDF	getCDF() Gets the CDF of a scalar distribution.
UnivariateGaussian.PDF	getDerivative() Gets the closed-form derivative of the function.
Double	inverse(double probability) Computes the inverse of the CDF for the given probability.

Methods inherited from class gov.sandia.cognition.statistics.distribution.UnivariateGaussian

clone, convertFromVector, convertToVector, convolve, getEstimator, getMaxSupport, getMean, getMinSupport, getProbabilityFunction, getVariance, sample, setMean, setVariance, times, toString

Methods inherited from class gov.sandia.cognition.statistics.AbstractDistribution

sample

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface gov.sandia.cognition.statistics.SmoothUnivariateDistribution

getMean, getProbabilityFunction

Methods inherited from interface gov.sandia.cognition.statistics.UnivariateDistribution

getMaxSupport, getMinSupport, getVariance

Methods inherited from interface gov.sandia.cognition.statistics.Distribution

sample, sample

Methods inherited from interface gov.sandia.cognition.math.matrix.Vectorizable

clone, convertFromVector, convertToVector

Constructor Detail

UnivariateGaussian.CDF

public UnivariateGaussian.CDF()

Creates a new instance of UnivariateGaussian with zero mean and unit variance

UnivariateGaussian.CDF

public UnivariateGaussian.CDF(double mean,
                              double variance)

Creates a new instance of UnivariateGaussian

Parameters:

mean - First central moment (expectation) of the distribution

variance - Second central moment (square of standard deviation) of the distribution

UnivariateGaussian.CDF

public UnivariateGaussian.CDF(UnivariateGaussian other)

Copy constructor

Parameters:

other - UnivariateGaussian to copy

Method Detail

evaluate

public Double evaluate(Double input)

Description copied from interface: Evaluator

Evaluates the function on the given input and returns the output.

Specified by:

evaluate in interface Evaluator<Double,Double>

Parameters:

input - The input to evaluate.

Returns:

The output produced by evaluating the input.

evaluateAsDouble

public double evaluateAsDouble(Double input)

Description copied from interface: ScalarFunction

Evaluates the scalar function as a double.

Specified by:

evaluateAsDouble in interface ScalarFunction<Double>

Parameters:

input - The input value.

Returns:

The scalar output calculated from the given input.

evaluate

public double evaluate(double z)

Description copied from interface: UnivariateScalarFunction

Produces a double output for the given double input

Specified by:

evaluate in interface UnivariateScalarFunction

Parameters:

z - Input to the Evaluator

Returns:

output at the given input

evaluate

public static double evaluate(double z,
                              double mean,
                              double variance)

Computes the cumulative distribution of a Normalized Gaussian distribution using the errorFunction method. cdf(0) = 0.5, cdf(-infinity) = 0, cdf(infinity) = 1

Parameters:

mean - Mean of the PDF

variance - Variance of the PDF

z - value to compute the Gaussian cdf at

Returns:

integral( -infinity, z, gaussian(0,1) ) will be [0,1]

getCDF

public UnivariateGaussian.CDF getCDF()

Description copied from interface: UnivariateDistribution

Gets the CDF of a scalar distribution.

Specified by:

getCDF in interface ClosedFormUnivariateDistribution<Double>

Specified by:

getCDF in interface SmoothUnivariateDistribution

Specified by:

getCDF in interface UnivariateDistribution<Double>

Overrides:

getCDF in class UnivariateGaussian

Returns:

CDF of the scalar distribution.

getDerivative

public UnivariateGaussian.PDF getDerivative()

Description copied from interface: ClosedFormDifferentiableEvaluator

Gets the closed-form derivative of the function.

Specified by:

getDerivative in interface ClosedFormDifferentiableEvaluator<Double,Double,Double>

Specified by:

getDerivative in interface SmoothCumulativeDistributionFunction

Returns:

Closed-form derivative of the function.

differentiate

public Double differentiate(Double input)

Description copied from interface: DifferentiableEvaluator

Differentiates the output with respect to the input

Specified by:

differentiate in interface DifferentiableEvaluator<Double,Double,Double>

Parameters:

input - Input about which to compute the derivative

Returns:

Derivative of the output with respect to the given input

inverse

public Double inverse(double probability)

Description copied from interface: InvertibleCumulativeDistributionFunction

Computes the inverse of the CDF for the given probability. That is, compute the value "x" such that p=CDF(x).

Specified by:

inverse in interface InvertibleCumulativeDistributionFunction<Double>

Parameters:

probability - Probability to invert.

Returns:

Inverse of the CDF for the given probability.