Package org.drip.sequence.metrics

Class SingleSequenceAgnosticMetrics

java.lang.Object

org.drip.sequence.metrics.SingleSequenceAgnosticMetrics

Direct Known Subclasses:

BoundedSequenceAgnosticMetrics, IntegerSequenceAgnosticMetrics, PoissonSequenceAgnosticMetrics

public class SingleSequenceAgnosticMetrics
extends java.lang.Object

SingleSequenceAgnosticMetrics contains the Sample Distribution Metrics and Agnostic Bounds related to the specified Sequence.

• Module = Numerical Core Module
• Library = Statistical Learning Library
• Project = Sequence
• Package = Metrics

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
SingleSequenceAgnosticMetrics(double[] adblSequence, R1Univariate distPopulation)	Build out the Sequence and their Metrics

Method Summary

Modifier and Type	Method	Description
PivotedDepartureBounds	centralMomentBound(double dblLevel, int iMoment)	Retrieve the Mean Departure Bounds Using the Central Moment Bounding Inequality
PivotedDepartureBounds	chebyshevAssociationBound(R1ToR1 au1, boolean bNonDecreasing1, R1ToR1 au2, boolean bNonDecreasing2)	Retrieve the Chebyshev's Association Joint Expectation Bound
PivotedDepartureBounds	chebyshevBound(double dblLevel)	Retrieve the Mean Departure Bounds Using the Chebyshev's Inequality
PivotedDepartureBounds	chebyshevCantelliBound(double dblLevel)	Retrieve the Mean Departure Bounds Using the Chebyshev-Cantelli Inequality
double	empiricalAnchorMoment(int iMoment, double dblAnchor, boolean bAbsolute)	Compute the Specified Anchor Moment of the Sample Sequence
double	empiricalCentralMoment(int iMoment, boolean bAbsolute)	Compute the Specified Central Moment of the Sample Sequence
double	empiricalExpectation()	Retrieve the Sample Expectation
double	empiricalRawMoment(int iMoment, boolean bAbsolute)	Compute the Specified Raw Moment of the Sample Sequence
double	empiricalVariance()	Retrieve the Sample Variance
SingleSequenceAgnosticMetrics	functionSequenceMetrics(R1ToR1 au)	Generate the Metrics for the Univariate Function Sequence
boolean	isPositive()	Retrieve the Sequence Positiveness Flag
double	markovUpperProbabilityBound(double dblLevel, R1ToR1 auNonDecreasing)	Retrieve the Markov Upper Limiting Probability Bound for the Specified Level: - P (X gte t) lte E[f(X)] / f(t)
R1Univariate	populationDistribution()	Retrieve the Population Distribution
double	populationMean()	Retrieve the Population Mean
double	populationVariance()	Retrieve the Population Variance
double[]	sequence()	Retrieve the Input Sequence
PivotedDepartureBounds	weakLawAverageBounds(double dblLevel)	Estimate Mean Departure Bounds of the Average using the Weak Law of Large Numbers

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

SingleSequenceAgnosticMetrics

public SingleSequenceAgnosticMetrics(double[] adblSequence,
R1Univariate distPopulation)
                              throws java.lang.Exception

Build out the Sequence and their Metrics

Parameters:

adblSequence - Array of Sequence Entries

distPopulation - The True Underlying Generator Distribution of the Population

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

empiricalCentralMoment

public double empiricalCentralMoment(int iMoment,
boolean bAbsolute)
                              throws java.lang.Exception

Compute the Specified Central Moment of the Sample Sequence

Parameters:

iMoment - The Moment

bAbsolute - TRUE - The Moment sought is on the Absolute Value

Returns:

The Specified Central Moment of the Sample Sequence

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

empiricalRawMoment

public double empiricalRawMoment(int iMoment,
boolean bAbsolute)
                          throws java.lang.Exception

Compute the Specified Raw Moment of the Sample Sequence

Parameters:

iMoment - The Moment

bAbsolute - TRUE - The Moment sought is on the Absolute Value

Returns:

The Specified Raw Moment of the Sample Sequence

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

empiricalAnchorMoment

public double empiricalAnchorMoment(int iMoment,
double dblAnchor,
boolean bAbsolute)
                             throws java.lang.Exception

Compute the Specified Anchor Moment of the Sample Sequence

Parameters:

iMoment - The Moment

dblAnchor - The Anchor Pivot off of which the Moment is calculated

bAbsolute - TRUE - The Moment sought is on the Absolute Value

Returns:

The Specified Anchor Moment of the Sample Sequence

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

functionSequenceMetrics

public SingleSequenceAgnosticMetrics functionSequenceMetrics(R1ToR1 au)

Generate the Metrics for the Univariate Function Sequence

Parameters:

au - The Univariate Function

Returns:

Metrics for the Univariate Function Sequence

populationDistribution

public R1Univariate populationDistribution()

Retrieve the Population Distribution

Returns:

The Population Distribution

empiricalExpectation

public double empiricalExpectation()

Retrieve the Sample Expectation

Returns:

The Sample Expectation

populationMean

public double populationMean()
                      throws java.lang.Exception

Retrieve the Population Mean

Returns:

The Population Mean

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

empiricalVariance

public double empiricalVariance()

Retrieve the Sample Variance

Returns:

The Sample Variance

populationVariance

public double populationVariance()
                          throws java.lang.Exception

Retrieve the Population Variance

Returns:

The Population Variance

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

isPositive

public boolean isPositive()

Retrieve the Sequence Positiveness Flag

Returns:

TRUE - The Sequence is Positiveness

sequence

public double[] sequence()

Retrieve the Input Sequence

Returns:

The Input Sequence

markovUpperProbabilityBound

public double markovUpperProbabilityBound(double dblLevel,
R1ToR1 auNonDecreasing)
                                   throws java.lang.Exception

Retrieve the Markov Upper Limiting Probability Bound for the Specified Level: - P (X gte t) lte E[f(X)] / f(t)

Parameters:

dblLevel - The Specified Level

auNonDecreasing - The Non-decreasing Bounding Transformer Function

Returns:

The Markov Upper Limiting Probability Bound for the Specified Level

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

chebyshevBound

public PivotedDepartureBounds chebyshevBound(double dblLevel)

Retrieve the Mean Departure Bounds Using the Chebyshev's Inequality

Parameters:

dblLevel - The Level at which the Departure is sought

Returns:

The Mean Departure Bounds Instance

centralMomentBound

public PivotedDepartureBounds centralMomentBound(double dblLevel,
int iMoment)

Retrieve the Mean Departure Bounds Using the Central Moment Bounding Inequality

Parameters:

dblLevel - The Level at which the Departure is sought

iMoment - The Moment Bound sought

Returns:

The Mean Departure Bounds Instance

chebyshevCantelliBound

public PivotedDepartureBounds chebyshevCantelliBound(double dblLevel)

Retrieve the Mean Departure Bounds Using the Chebyshev-Cantelli Inequality

Parameters:

dblLevel - The Level at which the Departure is sought

Returns:

The Mean Departure Bounds

chebyshevAssociationBound

public PivotedDepartureBounds chebyshevAssociationBound(R1ToR1 au1,
boolean bNonDecreasing1,
R1ToR1 au2,
boolean bNonDecreasing2)

Retrieve the Chebyshev's Association Joint Expectation Bound

Parameters:

au1 - Function 1 Operating On Sequence 1

bNonDecreasing1 - TRUE - Function 1 is non-decreasing

au2 - Function 2 Operating On Sequence 2

bNonDecreasing2 - TRUE - Function 2 is non-decreasing

Returns:

The Chebyshev's Association Joint Expectation Bound

weakLawAverageBounds

public PivotedDepartureBounds weakLawAverageBounds(double dblLevel)

Estimate Mean Departure Bounds of the Average using the Weak Law of Large Numbers

Parameters:

dblLevel - The Level at which the Departure is sought

Returns:

The Mean Departure Bounds