Uses of Interface
org.drip.function.definition.R2ToR1

Packages that use R2ToR1

Package	Description
org.drip.dynamics.ito	Ito Stochastic Process Dynamics Foundation
org.drip.dynamics.physical	Implementation of Physical Process Dynamics
org.drip.dynamics.process	Ito-Dynamics Based Stochastic Process
org.drip.function.definition	Function Implementation Ancillary Support Objects
org.drip.measure.chisquare	Chi-Square Distribution Implementation/Properties
org.drip.measure.gamma	R1 Gamma Distribution Implementation/Properties
org.drip.measure.transform	Expressing one Measure Using Another
org.drip.numerical.estimation	Function Numerical Estimates/Corrections/Bounds
org.drip.specialfunction.bessel	Ordered Bessel Function Variant Estimators
org.drip.specialfunction.beta	Estimation Techniques for Beta Function
org.drip.specialfunction.definition	Definition of Special Function Estimators
org.drip.specialfunction.derived	Special Functions Derived using Others
org.drip.specialfunction.generator	Special Function Series Term Generators
org.drip.specialfunction.hypergeometric	Hyper-geometric Function Estimation Schemes
org.drip.specialfunction.ode	Special Function Ordinary Differential Equations

Uses of R2ToR1 in org.drip.dynamics.ito

Classes in org.drip.dynamics.ito that implement R2ToR1

Modifier and Type	Class	Description
class	R1ToR1Drift	R1ToR1Drift implements the R1 to R1 Drift Function.
class	R1ToR1Volatility	R1ToR1Volatility implements the R1 to R1 Volatility Function.

Uses of R2ToR1 in org.drip.dynamics.physical

Classes in org.drip.dynamics.physical that implement R2ToR1

Modifier and Type	Class	Description
class	R1WhiteThermalFrictionalNoise	R1WhiteThermalFrictionalNoise implements the Volatility Function induced by the Background Thermal Noise in a Friction-Elastic System.

Uses of R2ToR1 in org.drip.dynamics.process

Classes in org.drip.dynamics.process that implement R2ToR1

Modifier and Type	Class	Description
class	R1ProbabilityDensityFunction	R1ProbabilityDensityFunction exposes the R1 Probability Density Function Evaluation Equation.
class	R1ProbabilityDensityFunctionCIR	R1ProbabilityDensityFunctionCIR exposes the R1 Probability Density Function Evaluation Equation for an Underlying CIR Process.

Uses of R2ToR1 in org.drip.function.definition

Methods in org.drip.function.definition that return R2ToR1

Modifier and Type	Method	Description
R2ToR1	R2ToR1Property.r2ToR1Left()	Retrieve the Left R2 To R1 Function
R2ToR1	R2ToR1Property.r2ToR1Right()	Retrieve the Right R2 To R1 Function

Constructors in org.drip.function.definition with parameters of type R2ToR1

Constructor	Description
R2ToR1Property(java.lang.String type, R2ToR1 r2ToR1Left, R2ToR1 r2ToR1Right, double mismatchTolerance)	R2ToR1Property Constructor

Uses of R2ToR1 in org.drip.measure.chisquare

Methods in org.drip.measure.chisquare that return R2ToR1

Modifier and Type	Method	Description
R2ToR1	R1Central.lowerIncompleteGammaEstimator()	Retrieve the Lower Incomplete Gamma Estimator
R2ToR1	R1NonCentral.lowerIncompleteGammaEstimator()	Retrieve the Lower Incomplete Gamma Estimator

Methods in org.drip.measure.chisquare with parameters of type R2ToR1

Modifier and Type	Method	Description
static R1NonCentralCumulantInvariant	R1NonCentralCumulantInvariant.InvariantFourthCumulant(int degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Fourth Cumulant Invariant Instance of R1NonCentralCumulantInvariant
static R1NonCentralCumulantInvariant	R1NonCentralCumulantInvariant.InvariantSecondCumulant(int degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Second Cumulant Invariant Instance of R1NonCentralCumulantInvariant
static R1NonCentralCumulantInvariant	R1NonCentralCumulantInvariant.InvariantThirdCumulant(int degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Third Cumulant Invariant Instance of R1NonCentralCumulantInvariant
static R1NonCentral	R1NonCentral.Standard(double degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Standard Instance of R1NonCentral

Constructors in org.drip.measure.chisquare with parameters of type R2ToR1

Constructor	Description
R1Central(double degreesOfFreedom, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	R1Central Constructor
R1NonCentral(R1NonCentralParameters r1NonCentralParameters, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	R1NonCentral Constructor
R1NonCentralCumulantInvariant(R1NonCentralParameters r1NonCentralParameters, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator, double sankaranB)	R1NonCentralCumulantInvariant Constructor

Uses of R2ToR1 in org.drip.measure.gamma

Methods in org.drip.measure.gamma that return R2ToR1

Modifier and Type	Method	Description
R2ToR1	R1ShapeScaleDistribution.lowerIncompleteGammaEstimator()	Retrieve the Lower Incomplete Gamma Estimator

Methods in org.drip.measure.gamma with parameters of type R2ToR1

Modifier and Type	Method	Description
static R1ShapeScaleDistribution	R1ShapeScaleDistribution.ShapeRate(double shapeParameter, double rateParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	Construct a Gamma Distribution from Shape and Rate Parameters
static R1ShapeScaleDistribution	R1ShapeScaleDistribution.ShapeSummation(double[] shapeParameterArray, double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	Shape Summation Based ShapeScaleDistribution
static R1ShapeScaleDistribution	R1ShapeScaleDistribution.Standard(double shapeParameter, double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	Construct the Standard R1ShapeScaleDistribution Instance

Constructors in org.drip.measure.gamma with parameters of type R2ToR1

Constructor	Description
ErlangDistribution(int shapeParameter, double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	ErlangDistribution Constructor
R1ShapeScaleDiscrete(double shapeParameter, double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, int randomGenerationScheme)	R1ShapeScaleDiscrete Constructor
R1ShapeScaleDistribution(ShapeScaleParameters shapeScaleParameters, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	R1ShapeScaleDistribution Constructor

Uses of R2ToR1 in org.drip.measure.transform

Constructors in org.drip.measure.transform with parameters of type R2ToR1

Constructor	Description
R1GammaToExponential(double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	R1GammaToExponential Constructor
R1GammaToMaxwellBoltzmannSquared(double a, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)	R1GammaToMaxwellBoltzmannSquared Constructor

Uses of R2ToR1 in org.drip.numerical.estimation

Classes in org.drip.numerical.estimation that implement R2ToR1

Modifier and Type	Class	Description
class	R2ToR1Estimator	R2ToR1Estimator exposes the Stubs behind R2 - R1 Approximate Numerical Estimators.

Uses of R2ToR1 in org.drip.specialfunction.bessel

Classes in org.drip.specialfunction.bessel that implement R2ToR1

Modifier and Type	Class	Description
class	FirstFrobeniusSeriesEstimator	FirstFrobeniusSeriesEstimator implements the Frobenius Series Estimator for the Cylindrical Bessel Function of the First Kind.
class	FirstSchlafliIntegralEstimator	FirstSchlafliIntegralEstimator implements the Integral Estimator for the Cylindrical Bessel Function of the First Kind.
class	ModifiedFirstFrobeniusSeriesEstimator	ModifiedFirstFrobeniusSeriesEstimator implements the Frobenius Series Estimator for the Modified Bessel Function of the First Kind.
class	ModifiedFirstHankelAsymptoteEstimator	ModifiedFirstHankelAsymptoteEstimator implements the Hankel Large z Asymptote Series Estimator for the Modified Bessel Function of the First Kind.
class	ModifiedFirstIntegralEstimator	ModifiedFirstIntegralEstimator implements the Integral Estimator for the Modified Bessel Function of the First Kind.
class	ModifiedSecondEstimator	ModifiedSecondEstimator implements the Estimator for the Modified Bessel Function of the Second Kind.
class	ModifiedSecondHankelAsymptoteEstimator	ModifiedSecondHankelAsymptoteEstimator implements the Hankel Large z Asymptote Series Estimator for the Modified Bessel Function of the Second Kind.
class	ModifiedSecondIntegralEstimator	ModifiedSecondIntegralEstimator implements the Integral Estimator for the Modified Bessel Function of the Second Kind.
class	RiccatiCEstimator	RiccatiCEstimator implements the Riccati-Bessel C Function Estimator using the Cylindrical Bessel Function of the First Kind.
class	RiccatiSEstimator	RiccatiSEstimator implements the Riccati-Bessel S Function Estimator using the Cylindrical Bessel Function of the First Kind.
class	SecondNISTSeriesEstimator	SecondNISTSeriesEstimator implements the NIST Series Estimator for the Cylindrical Bessel Function of the Second Kind.
class	SecondWatsonIntegralEstimator	SecondWatsonIntegralEstimator implements the Integral Estimator for the Cylindrical Bessel Function of the Second Kind.
class	SecondWeberEstimator	SecondWeberEstimator implements the Weber Estimation for the Cylindrical Bessel Function of the Second Kind.
class	SphericalFirstEstimator	SphericalFirstEstimator implements the Integral Estimator for the Spherical Bessel Function of the First Kind.
class	SphericalSecondEstimator	SphericalSecondEstimator implements the Integral Estimator for the Spherical Bessel Function of the Second Kind.

Uses of R2ToR1 in org.drip.specialfunction.beta

Classes in org.drip.specialfunction.beta that implement R2ToR1

Modifier and Type	Class	Description
class	IntegrandEstimator	IntegrandEstimator implements the Beta Function using Integrand Estimation Schemes.
class	LogGammaEstimator	LogGammaEstimator implements the Log Beta Function using the Log Gamma Function.
class	SummationSeriesEstimator	SummationSeriesEstimator implements the Summation Series Based Beta Estimation.

Methods in org.drip.specialfunction.beta that return R2ToR1

Modifier and Type	Method	Description
static R2ToR1	AsymptoticLogEstimator.LargeX(R1ToR1 logGammaEstimator)	Construct the Large X Asymptote Estimate for the Log Beta Function
static R2ToR1	AsymptoticLogEstimator.Stirling()	Construct the Stirling Asymptote Estimate for the Log Beta Function

Methods in org.drip.specialfunction.beta with parameters of type R2ToR1

Modifier and Type	Method	Description
static double	CombinatorialEstimate.BetaBinomial(double n, double k, R2ToR1 betaEstimator)	Estimate the Binomial Coefficient Using the Beta Function

Uses of R2ToR1 in org.drip.specialfunction.definition

Classes in org.drip.specialfunction.definition that implement R2ToR1

Modifier and Type	Class	Description
class	BesselFirstKindEstimator	BesselFirstKindEstimator exposes the Estimator for the Bessel Function of the First Kind.
class	BesselSecondKindEstimator	BesselSecondKindEstimator exposes the Estimator for the Bessel Function of the Second Kind.
class	BetaEstimator	BetaEstimator exposes the Stubs for estimating Beta Function and its Jacobian.
class	ModifiedBesselFirstKindEstimator	ModifiedBesselFirstKindEstimator exposes the Estimator for the Modified Bessel Function of the First Kind.
class	ModifiedBesselSecondKindEstimator	ModifiedBesselSecondKindEstimator exposes the Estimator for the Modified Bessel Function of the Second Kind.
class	RiccatiBesselCEstimator	RiccatiBesselCEstimator exposes the Estimator for the Riccati-Bessel C Function.
class	RiccatiBesselSEstimator	RiccatiBesselSEstimator exposes the Estimator for the Riccati-Bessel S Function.
class	SphericalBesselFirstKindEstimator	SphericalBesselFirstKindEstimator exposes the Estimator for the Spherical Bessel Function of the First Kind.
class	SphericalBesselSecondKindEstimator	SphericalBesselSecondKindEstimator exposes the Estimator for the Spherical Bessel Function of the Second Kind.

Uses of R2ToR1 in org.drip.specialfunction.derived

Constructors in org.drip.specialfunction.derived with parameters of type R2ToR1

Constructor	Description
EllipticEIntegral(R2ToR1 logBetaEstimator, int quadratureCount)	EllipticEIntegral Constructor
EllipticKIntegral(R2ToR1 logBetaEstimator, int quadratureCount)	EllipticKIntegral Constructor
Jacobi(double alpha, double beta, int n, R2ToR1 logBetaEstimator, int quadratureCount)	Jacobi Constructor
Legendre(double alpha, double ceta, R2ToR1 logBetaEstimator, int quadratureCount, R1ToR1 gammaEstimator)	Legendre Constructor

Uses of R2ToR1 in org.drip.specialfunction.generator

Classes in org.drip.specialfunction.generator that implement R2ToR1

Modifier and Type	Class	Description
class	BesselFirstKindLaurentExpansion	BesselFirstKindLaurentExpansion implements the Laurent-Series Generating Function and the Expansion Terms for the Cylindrical Bessel Function of the First Kind.
class	SeriesExpansion	SeriesExpansion implements the Generating Function and the Expansion Terms for the specified Special Function.
class	SphericalBesselFirstKindExpansion	SphericalBesselFirstKindExpansion implements the Generating Function and the Expansion Terms for the Spherical Bessel Function of the First Kind.
class	SphericalBesselSecondKindExpansion	SphericalBesselSecondKindExpansion implements the Generating Function and the Expansion Terms for the Spherical Bessel Function of the Second Kind.

Uses of R2ToR1 in org.drip.specialfunction.hypergeometric

Methods in org.drip.specialfunction.hypergeometric that return R2ToR1

Modifier and Type	Method	Description
R2ToR1	EulerQuadratureEstimator.logBetaEstimator()	Retrieve the Log Beta Estimator

Constructors in org.drip.specialfunction.hypergeometric with parameters of type R2ToR1

Constructor	Description
EulerQuadratureEstimator(HypergeometricParameters hypergeometricParameters, R2ToR1 logBetaEstimator, int quadratureCount)	EulerQuadratureEstimator Constructor

Uses of R2ToR1 in org.drip.specialfunction.ode

Methods in org.drip.specialfunction.ode that return R2ToR1

Modifier and Type	Method	Description
R2ToR1	SecondOrder.firstDerivativeCoefficient()	Retrieve the R2 to R1 First Derivative Coefficient Function
R2ToR1	SecondOrder.secondDerivativeCoefficient()	Retrieve the R2 to R1 Second Derivative Coefficient Function
R2ToR1	SecondOrder.zeroDerivativeCoefficient()	Retrieve the R2 to R1 Zero Derivative Coefficient Function

Constructors in org.drip.specialfunction.ode with parameters of type R2ToR1

Constructor	Description
SecondOrder(R2ToR1 secondDerivativeCoefficient, R2ToR1 firstDerivativeCoefficient, R2ToR1 zeroDerivativeCoefficient)	SecondOrder Constructor