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# Detection

## •Functions and parameters contained in this package:

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### •Package functions and their basic documentation along with simple examples

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#### •Central

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#### •CentralToNonCentral

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This can be expressed in a more conventional form by writing μ for the mean and σ for the standard deviation.  We then use an abbreviated notation for higher order central moments:

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Arbitraty higher order expressions can easilly be generated:

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One practical purpose of this function is to transform data taken for the moments of a distribution from one form to another.  For example the data may be from explicit measurements of the pulse-to-pulse fluctuations of the radar cross section of a realistic target. These data can then be used to construct the LaplaceCharacteristicFunction for this target (using CentralMomentsToLaplaceCharacteristicFunction) which is then used in the EdgeworthDetectionExpansion or the EdgeworthProbabilityExpansion to construct a detection model for this target (using MakeEdgeworthDetectionExpansion or MakeEdgeworthDetectionExpansionCode).

#### •CoherentDetectorFunction

Usage message for CoherentDetectorFunction

#### •CorrelationMatrix

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#### •DetectionProbability

Coherent Detector

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Swerling 0

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Swerling 1

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Swerling 2

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Swerling 3

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Swerling 4

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versus snr at a value of for a single pulse:

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versus snr at a value of for a 10 pulses:

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#### •ExponentialCorrelationMatrix

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#### •GammaExpansion

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#### •GaussianCorrelationMatrix

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#### •GCFunction

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#### •LinearDetectorFunction

Usage message for LinearDetectorFunction

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#### •Models

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#### •MomentFunction

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#### •MomentMethod

The central moment of a probability distribution of one varialbe is where μ is the mean of the distribution.

The noncentral moment of a probability distribution of one varialbe is .

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#### •NonCentralToCentral

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This can be expressed in a more concisely using an abbreviated notation for higher order central moments: .

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Arbitraty higher order expressions can easilly be generated:

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As with the function CentralToNonCentral, one practical purpose of this function is to transform data taken for the moments of a distribution from one form to another.  For example the data may be from explicit measurements of the pulse-to-pulse fluctuations of the radar cross section of a realistic target. These data can then be used to construct the LaplaceCharacteristicFunction for this target (using CentralMomentsToLaplaceCharacteristicFunction) which is then used in the EdgeworthDetectionExpansion or the EdgeworthProbabilityExpansion to construct a detection model for this target (using MakeEdgeworthDetectionExpansion or MakeEdgeworthDetectionExpansionCode).

#### •PositiveIntegerOrExpressionQ

Usage message for PositiveIntegerOrExpressionQ

#### •PositiveOrExpressionQ

Usage message for PositiveOrExpressionQ

#### •ProbabilityOfDetection

Usage message for ProbabilityOfDetection

#### •ProbabilityOfFalseAlarm

Usage message for ProbabilityOfFalseAlarm

#### •ProbabilityOrExpressionQ

Usage message for ProbabilityOrExpressionQ

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#### •ProbabilityQWithMessage

Usage message for ProbabilityQWithMessage

#### •PureSymbolOrExpressionQ

Usage message for PureSymbolOrExpressionQ

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#### •SwerlingModel5

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