gov.sandia.cognition.statistics.method

Class ChebyshevInequality

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.method.ChebyshevInequality

All Implemented Interfaces:

ConfidenceIntervalEvaluator<java.util.Collection<java.lang.Double>>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

public class ChebyshevInequality
extends AbstractCloneableSerializable
implements ConfidenceIntervalEvaluator<java.util.Collection<java.lang.Double>>

Computes the Chebyshev Inequality for the given level of confidence. Answers the question: "What range of values can a random variable take if I can estimate its mean and variance at least confidence percent of the time?" 1-confidence = Pr{ abs(X-mean(data)) >= a } <= variance(data) / a^2 -> Pr{ mean-a <= X <= mean+a } >= confidence

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static ChebyshevInequality	INSTANCE This class has no members, so here's a static instance.

Constructor Summary

Constructors

Constructor and Description
ChebyshevInequality() Creates a new instance of ChebyshevInequality

Method Summary

Modifier and Type	Method and Description
ConfidenceInterval	computeConfidenceInterval(java.util.Collection<java.lang.Double> data, double confidence) Computes the Chebyshev Inequality for the given level of confidence.
ConfidenceInterval	computeConfidenceInterval(double sampleMean, double sampleVariance, int numSamples, double confidence) Computes the Chebyshev Inequality for the given level of confidence.

Methods inherited from class gov.sandia.cognition.util.AbstractCloneableSerializable

clone

Methods inherited from class java.lang.Object

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

Field Detail

INSTANCE

public static final ChebyshevInequality INSTANCE

This class has no members, so here's a static instance.

Constructor Detail

ChebyshevInequality

public ChebyshevInequality()

Creates a new instance of ChebyshevInequality

Method Detail

computeConfidenceInterval

public ConfidenceInterval computeConfidenceInterval(java.util.Collection<java.lang.Double> data,
                                                    double confidence)

Computes the Chebyshev Inequality for the given level of confidence. Answers the question: "What range of values can a random variable take if I can estimate its mean and variance at least confidence percent of the time?" 1-confidence = Pr{ abs(X-mean(data)) >= a } <= variance(data) / a^2 -> Pr{ mean-a <= X <= mean+a } >= confidence

Specified by:

computeConfidenceInterval in interface ConfidenceIntervalEvaluator<java.util.Collection<java.lang.Double>>

Parameters:

data - Data from which to estimate the mean and variance

confidence - Confidence value to find the range of values for

Returns:

ConfidenceInterval describing the worst-case range that ANY random variable can take at the given confidence value

computeConfidenceInterval

public ConfidenceInterval computeConfidenceInterval(double sampleMean,
                                                    double sampleVariance,
                                                    int numSamples,
                                                    double confidence)

Computes the Chebyshev Inequality for the given level of confidence.

Specified by:

computeConfidenceInterval in interface ConfidenceIntervalEvaluator<java.util.Collection<java.lang.Double>>

Parameters:

sampleMean - The sample mean of the data

sampleVariance - The sample variance of the data

numSamples - The number of samples in the data

confidence - Confidence value to find the range of values for

Returns:

ConfidenceInterval describing the worst-case range that ANY random variable can take at the given confidence value