StableDistributionFeller (FsODE)

FsODE

Documentation for 0.0.2

StableDistributionFeller Type

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore.Redist.dll
Base Type: StableDistributionBase

Constructors

Constructor	Description
`StableDistributionFeller()` Full Usage: `StableDistributionFeller()`	Creates a new instance of this distribution with default parameters (alpha=1, beta=0) and the default generator.
`StableDistributionFeller(generator)` Full Usage: `StableDistributionFeller(generator)` Parameters: generator : `Generator` - Random number generator to be used with this distribution.	Creates a new instance of this distribution with default parameters (alpha=1, beta=0). generator : `Generator` Random number generator to be used with this distribution.
`StableDistributionFeller(alpha, gamma)` Full Usage: `StableDistributionFeller(alpha, gamma)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew).	Creates a new instance of this distribution with given parameters (alpha, beta) and the default random number generator. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew).
`StableDistributionFeller(alpha, gamma, aga)` Full Usage: `StableDistributionFeller(alpha, gamma, aga)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). aga : `float` - Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma.	Creates a new instance of this distribution with given parameters (alpha, beta, abe) and the default random number generator. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). aga : `float` Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma.
`StableDistributionFeller(alpha, gamma, scale, location)` Full Usage: `StableDistributionFeller(alpha, gamma, scale, location)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). scale : `float` - Scaling parameter (broadness of the distribution). location : `float` - Location of the distribution.	Creates a new instance of this distribution with given parameters (alpha, beta, scale, location) and the default random number generator. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). scale : `float` Scaling parameter (broadness of the distribution). location : `float` Location of the distribution.
`StableDistributionFeller(alpha, gamma, scale, location, generator)` Full Usage: `StableDistributionFeller(alpha, gamma, scale, location, generator)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). scale : `float` - Scaling parameter (broadness of the distribution). location : `float` - Location of the distribution. generator : `Generator` - Random number generator to be used with this distribution.	Creates a new instance of this distribution with given parameters (alpha, beta, scale, location) and the provided random number generator. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). scale : `float` Scaling parameter (broadness of the distribution). location : `float` Location of the distribution. generator : `Generator` Random number generator to be used with this distribution.
`StableDistributionFeller(alpha, gamma, aga, scale, location)` Full Usage: `StableDistributionFeller(alpha, gamma, aga, scale, location)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). aga : `float` - Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. scale : `float` - Scaling parameter (broadness of the distribution). location : `float` - Location of the distribution.	Creates a new instance of this distribution with given parameters (alpha, beta, abe, scale, location) and the default random number generator. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). aga : `float` Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. scale : `float` Scaling parameter (broadness of the distribution). location : `float` Location of the distribution.
`StableDistributionFeller(alpha, gamma, aga, scale, location, generator)` Full Usage: `StableDistributionFeller(alpha, gamma, aga, scale, location, generator)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). aga : `float` - Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. scale : `float` - Scaling parameter (broadness of the distribution). location : `float` - Location of the distribution. generator : `Generator` - Random number generator to be used with this distribution.	Creates a new instance of this distribution with given parameters (alpha, beta, abe, scale, location) and the provided random number generator. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). aga : `float` Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. scale : `float` Scaling parameter (broadness of the distribution). location : `float` Location of the distribution. generator : `Generator` Random number generator to be used with this distribution.

Instance members

Instance member	Description
`this.Initialize` Full Usage: `this.Initialize` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). aga : `float` - Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. scale : `float` - Scaling parameter (broadness of the distribution). location : `float` - Location of the distribution.	Initializes this instance of the distribution with the distribution parameters. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). aga : `float` Parameter to specify gamma with higher accuracy around it's limit(s). For an explanation how aga is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. scale : `float` Scaling parameter (broadness of the distribution). location : `float` Location of the distribution.
`this.Maximum` Full Usage: `this.Maximum` Returns: `float` Modifiers: abstract	Returns: `float`
`this.Mean` Full Usage: `this.Mean` Returns: `float` Modifiers: abstract	Returns: `float`
`this.Median` Full Usage: `this.Median` Returns: `float` Modifiers: abstract	Returns: `float`
`this.Minimum` Full Usage: `this.Minimum` Returns: `float` Modifiers: abstract	Returns: `float`
`this.Mode` Full Usage: `this.Mode` Returns: `float[]` Modifiers: abstract	Returns: `float[]`
`this.NextDouble` Full Usage: `this.NextDouble` Returns: `float` Modifiers: abstract	Returns: `float`
`this.PDF` Full Usage: `this.PDF` Parameters: x : `float` Returns: `float` Modifiers: abstract	x : `float` Returns: `float`
`this.Variance` Full Usage: `this.Variance` Returns: `float` Modifiers: abstract	Returns: `float`

Static members

Static member	Description
`StableDistributionFeller.CCDF(x, alpha, gamma)` Full Usage: `StableDistributionFeller.CCDF(x, alpha, gamma)` Parameters: x : `float` alpha : `float` gamma : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` Returns: `float`
`StableDistributionFeller.CCDF(x, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.CCDF(x, alpha, gamma, aga)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.CCDF(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.CCDF(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.CDF(x, alpha, gamma)` Full Usage: `StableDistributionFeller.CDF(x, alpha, gamma)` Parameters: x : `float` alpha : `float` gamma : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` Returns: `float`
`StableDistributionFeller.CDF(x, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.CDF(x, alpha, gamma, aga)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.CDF(x, alpha, gamma, tempStorage, precision)` Full Usage: `StableDistributionFeller.CDF(x, alpha, gamma, tempStorage, precision)` Parameters: x : `float` alpha : `float` gamma : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.CDF(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.CDF(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.CDFMethodForPositiveX(x, alpha, gamma, aga, tempStorage, precision, integFromXZero, integFromXInfinity, offs)` Full Usage: `StableDistributionFeller.CDFMethodForPositiveX(x, alpha, gamma, aga, tempStorage, precision, integFromXZero, integFromXInfinity, offs)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` integFromXZero : `byref<float>` integFromXInfinity : `byref<float>` offs : `byref<float>`	x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` integFromXZero : `byref<float>` integFromXInfinity : `byref<float>` offs : `byref<float>`
`StableDistributionFeller.GetAgaFromAlphaGamma(alpha, gamma)` Full Usage: `StableDistributionFeller.GetAgaFromAlphaGamma(alpha, gamma)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). gamma : `float` - Distribution parameter gamma (skew). Returns: `float` The parameter aga.	Aga is defined as follows: For alpha <=1, it is (alpha-gamma)/alpha (for gamma >=0) or (alpha+gamma)/alpha (for gamma <0). For alpha >1 it is 2-alpha-gamma (for gamma >=0) or 2-alpha+gamma (for gamma <0). This function calculates aga from alpha and gamma. alpha : `float` Distribution parameter alpha (broadness exponent). gamma : `float` Distribution parameter gamma (skew). Returns: `float` The parameter aga.
`StableDistributionFeller.GetAgt1GnParameterByGamma(x, alpha, gamma, aga, factorp, factorw, dev, logPrefactor)` Full Usage: `StableDistributionFeller.GetAgt1GnParameterByGamma(x, alpha, gamma, aga, factorp, factorw, dev, logPrefactor)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` factorp : `byref<float>` factorw : `byref<float>` dev : `byref<float>` logPrefactor : `byref<float>`	x : `float` alpha : `float` gamma : `float` aga : `float` factorp : `byref<float>` factorw : `byref<float>` dev : `byref<float>` logPrefactor : `byref<float>`
`StableDistributionFeller.GetAlt1GnParameterByGamma(x, alpha, gamma, aga, factorp, facdiv, dev, logPdfPrefactor)` Full Usage: `StableDistributionFeller.GetAlt1GnParameterByGamma(x, alpha, gamma, aga, factorp, facdiv, dev, logPdfPrefactor)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`	x : `float` alpha : `float` gamma : `float` aga : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`
`StableDistributionFeller.GetAlt1GpParameterByGamma(x, alpha, gamma, aga, factorp, facdiv, dev, logPdfPrefactor)` Full Usage: `StableDistributionFeller.GetAlt1GpParameterByGamma(x, alpha, gamma, aga, factorp, facdiv, dev, logPdfPrefactor)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`	x : `float` alpha : `float` gamma : `float` aga : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`
`StableDistributionFeller.GetGammaFromAlphaAga(alpha, aga, isGammaNegative)` Full Usage: `StableDistributionFeller.GetGammaFromAlphaAga(alpha, aga, isGammaNegative)` Parameters: alpha : `float` - Distribution parameter alpha (broadness exponent). aga : `float` - Aga is defined as follows: For alpha <=1, it is (alpha-gamma)/alpha (for gamma >=0) or (alpha+gamma)/alpha (for gamma <0). For alpha >1 it is 2-alpha-gamma (for gamma >=0) or 2-alpha+gamma (for gamma <0). isGammaNegative : `bool` - Because gamma is not defined by aga alone, you have to specify if gamma should be positive or negative. Returns: `float` Distribution parameter gamma.	Calculates gamma in dependence of alpha and aga. alpha : `float` Distribution parameter alpha (broadness exponent). aga : `float` Aga is defined as follows: For alpha <=1, it is (alpha-gamma)/alpha (for gamma >=0) or (alpha+gamma)/alpha (for gamma <0). For alpha >1 it is 2-alpha-gamma (for gamma >=0) or 2-alpha+gamma (for gamma <0). isGammaNegative : `bool` Because gamma is not defined by aga alone, you have to specify if gamma should be positive or negative. Returns: `float` Distribution parameter gamma.
`StableDistributionFeller.GetInvertedAlphaGammaAga(x, alpha, gamma, aga, alphainv, xinv, gammainv, againv)` Full Usage: `StableDistributionFeller.GetInvertedAlphaGammaAga(x, alpha, gamma, aga, alphainv, xinv, gammainv, againv)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` alphainv : `byref<float>` xinv : `byref<float>` gammainv : `byref<float>` againv : `byref<float>`	x : `float` alpha : `float` gamma : `float` aga : `float` alphainv : `byref<float>` xinv : `byref<float>` gammainv : `byref<float>` againv : `byref<float>`
`StableDistributionFeller.IsValidAlpha(alpha)` Full Usage: `StableDistributionFeller.IsValidAlpha(alpha)` Parameters: alpha : `float` Returns: `bool`	alpha : `float` Returns: `bool`
`StableDistributionFeller.IsValidGamma(alpha, gamma)` Full Usage: `StableDistributionFeller.IsValidGamma(alpha, gamma)` Parameters: alpha : `float` gamma : `float` Returns: `bool`	alpha : `float` gamma : `float` Returns: `bool`
`StableDistributionFeller.IsValidLocation(location)` Full Usage: `StableDistributionFeller.IsValidLocation(location)` Parameters: location : `float` Returns: `bool`	location : `float` Returns: `bool`
`StableDistributionFeller.IsValidScale(scale)` Full Usage: `StableDistributionFeller.IsValidScale(scale)` Parameters: scale : `float` Returns: `bool`	scale : `float` Returns: `bool`
`StableDistributionFeller.PDF(x, alpha, gamma)` Full Usage: `StableDistributionFeller.PDF(x, alpha, gamma)` Parameters: x : `float` alpha : `float` gamma : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` Returns: `float`
`StableDistributionFeller.PDF(x, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.PDF(x, alpha, gamma, aga)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.PDF(x, alpha, gamma, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDF(x, alpha, gamma, tempStorage, precision)` Parameters: x : `float` - The argument. alpha : `float` - First parameter of the distribution (StableDistributionFeller). gamma : `float` - Second parameter of the distribution (StableDistributionFeller). tempStorage : `byref<obj>` - precision : `float` - Relative precision goal for the calculation. Returns: `float`	Calculates the probability density using either series expansion for small or big arguments, or a integration in the intermediate range. x : `float` The argument. alpha : `float` First parameter of the distribution (StableDistributionFeller). gamma : `float` Second parameter of the distribution (StableDistributionFeller). tempStorage : `byref<obj>` precision : `float` Relative precision goal for the calculation. Returns: `float`
`StableDistributionFeller.PDF(x, alpha, gamma, aga, scale, pos, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDF(x, alpha, gamma, aga, scale, pos, tempStorage, precision)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` scale : `float` pos : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` scale : `float` pos : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDF(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDF(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - The argument. alpha : `float` - gamma : `float` - aga : `float` - For alpha <=1: This is either (alpha-gamma)/alpha for gamma >=0, or (alpha+gamma)/alpha for gamma < 1. tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculates the probability density using either series expansion for small or big arguments, or a integration in the intermediate range. x : `float` The argument. alpha : `float` gamma : `float` aga : `float` For alpha <=1: This is either (alpha-gamma)/alpha for gamma >=0, or (alpha+gamma)/alpha for gamma < 1. tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaBetween01And02(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFAlphaBetween01And02(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculation of the PDF if alpha is inbetween 0.1 and 0.2. For small x (1E-16), the accuracy at alpha=0.1 is only 1E-7. x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaBetween02And099(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFAlphaBetween02And099(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculation of the PDF if alpha is inbetween 0.2 and 0.99. For small x (1E-8), the accuracy at alpha=0.2 is only 1E-7. x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaBetween099And101(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFAlphaBetween099And101(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculation of the PDF if alpha is inbetween 0.99 and 1.01. x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaBetween0And01(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFAlphaBetween0And01(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculation of the PDF if alpha is inbetween 0.0 and 0.1. x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaBetween101And199999(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFAlphaBetween101And199999(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculation of the PDF if alpha is inbetween 1.01 and 1.99999. x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaBetween199999And2(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFAlphaBetween199999And2(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - tempStorage : `byref<obj>` - precision : `float` - Returns: `float`	Calculation of the PDF if alpha is inbetween 1.99999 and 2. For small x ( max 7), the asymptotic expansion is used. For big x, the maximum value resulting from direct integration and series expansion w.r.t. alpha is used. x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFAlphaEqualOne(x, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.PDFAlphaEqualOne(x, alpha, gamma, aga)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.PDFIntegral(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegral(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralA1(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralA1(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special version of the PDF-Integral for 0.99>=alpha<1. x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAgt1Gn(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAgt1Gn(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha>1 and gamma near to alpha-2 (i.e. gamma at the negative border). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAgt1GnD(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAgt1GnD(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha>1 and gamma near to alpha-2 (i.e. gamma at the negative border). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAgt1GnI(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAgt1GnI(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha>1 and gamma near to alpha-2 (i.e. gamma at the negative border). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAlt1Gn(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAlt1Gn(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha < 1 and gamma near to -alpha (i.e. gamma at the negative border). Here gamma was set to -alpha(1-dev2/Pi). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAlt1GnD(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAlt1GnD(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha < 1 and gamma near to -alpha (i.e. gamma at the negative border). Here gamma was set to -alpha(1-dev2/Pi). The core function is decreasing. x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAlt1GnI(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAlt1GnI(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha < 1 and gamma near to -alpha (i.e. gamma at the negative border). Here gamma was set to -alpha(1-dev2/Pi). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAlt1Gp(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAlt1Gp(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha < 1 and gamma near to +alpha (i.e. gamma at the positive border). Here gamma was set to alpha(1-dev2/Pi). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAlt1GpD(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAlt1GpD(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha < 1 and gamma near to +alpha (i.e. gamma at the positive border). Here gamma was set to alpha(1-dev2/Pi). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFIntegralAlt1GpI(x, alpha, gamma, aga, temp, precision)` Full Usage: `StableDistributionFeller.PDFIntegralAlt1GpI(x, alpha, gamma, aga, temp, precision)` Parameters: x : `float` - alpha : `float` - gamma : `float` - aga : `float` - temp : `byref<obj>` - precision : `float` - Returns: `float`	Special case for alpha < 1 and gamma near to +alpha (i.e. gamma at the positive border). Here gamma was set to alpha(1-dev2/Pi). x : `float` alpha : `float` gamma : `float` aga : `float` temp : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.PDFSeriesBigXFeller(z, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.PDFSeriesBigXFeller(z, alpha, gamma, aga)` Parameters: z : `float` - alpha : `float` - gamma : `float` - aga : `float` - Returns: `float`	Series expansion for big x, Feller parametrization. x should be > 0. z : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.PDFSeriesSmallXFeller(z, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.PDFSeriesSmallXFeller(z, alpha, gamma, aga)` Parameters: z : `float` - Circular frequency. alpha : `float` - Beta parameter. gamma : `float` - aga : `float` - Returns: `float` Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies, or double.NaN if the series not converges.	Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies. This is the imaginary part of the Fourier transform (in Mathematica notation): Im[Integrate[D[Exp[-t^beta],t]*Exp[-I w t],{t, 0, Infinity}]]. The sign of the return value here is positive!. z : `float` Circular frequency. alpha : `float` Beta parameter. gamma : `float` aga : `float` Returns: `float` Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies, or double.NaN if the series not converges.
`StableDistributionFeller.PDFTaylorExpansionAroundAlphaOne(x, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.PDFTaylorExpansionAroundAlphaOne(x, alpha, gamma, aga)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.PDFforPositiveX(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.PDFforPositiveX(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` - The argument. alpha : `float` - gamma : `float` - The gamma value. aga : `float` - For alpha <=1: This is either (alpha-gamma)/alpha for gamma >=0, or (alpha+gamma)/alpha for gamma < 1. For alpha >1, this is either (alpha-gamma) for gamma > (alpha-1), or (2-alpha+gamma) for gamma < (alpha-1). tempStorage : `byref<obj>` - Object that can be used to speed up subsequent calculations of the function. At first use, provide an object initialized with and then provide this object in subsequent calls of this function. precision : `float` - Relative precision goal. Returns: `float`	Calculates the probability density using either series expansion for small or big arguments, or a integration in the intermediate range. x : `float` The argument. alpha : `float` gamma : `float` The gamma value. aga : `float` For alpha <=1: This is either (alpha-gamma)/alpha for gamma >=0, or (alpha+gamma)/alpha for gamma < 1. For alpha >1, this is either (alpha-gamma) for gamma > (alpha-1), or (2-alpha+gamma) for gamma < (alpha-1). tempStorage : `byref<obj>` Object that can be used to speed up subsequent calculations of the function. At first use, provide an object initialized with and then provide this object in subsequent calls of this function. precision : `float` Relative precision goal. Returns: `float`
`StableDistributionFeller.PDFforXZero(alpha, gamma, aga)` Full Usage: `StableDistributionFeller.PDFforXZero(alpha, gamma, aga)` Parameters: alpha : `float` - Characteristic exponent of the distibution. gamma : `float` - Skewness parameter gamma. aga : `float` - 'Alternative gamma' value to specify gamma with enhanced accuracy. For an explanation how it is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. Returns: `float` Probability density value at x=0 for the stable distribution in Feller's parametrization.	Calculates the probability density at x=0 for the stable distribution in Feller's parametrization. alpha : `float` Characteristic exponent of the distibution. gamma : `float` Skewness parameter gamma. aga : `float` 'Alternative gamma' value to specify gamma with enhanced accuracy. For an explanation how it is defined, see StableDistributionFeller.GetAgaFromAlphaGamma. Returns: `float` Probability density value at x=0 for the stable distribution in Feller's parametrization.
`StableDistributionFeller.Quantile(p, alpha, gamma)` Full Usage: `StableDistributionFeller.Quantile(p, alpha, gamma)` Parameters: p : `float` alpha : `float` gamma : `float` Returns: `float`	p : `float` alpha : `float` gamma : `float` Returns: `float`
`StableDistributionFeller.Quantile(p, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.Quantile(p, alpha, gamma, aga)` Parameters: p : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	p : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.Quantile(p, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.Quantile(p, alpha, gamma, aga, tempStorage, precision)` Parameters: p : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	p : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.QuantileCCDF(p, alpha, gamma)` Full Usage: `StableDistributionFeller.QuantileCCDF(p, alpha, gamma)` Parameters: p : `float` alpha : `float` gamma : `float` Returns: `float`	p : `float` alpha : `float` gamma : `float` Returns: `float`
`StableDistributionFeller.QuantileCCDF(p, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.QuantileCCDF(p, alpha, gamma, aga)` Parameters: p : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	p : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.QuantileCCDF(q, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.QuantileCCDF(q, alpha, gamma, aga, tempStorage, precision)` Parameters: q : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	q : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionFeller.XZCDF(x, alpha, gamma)` Full Usage: `StableDistributionFeller.XZCDF(x, alpha, gamma)` Parameters: x : `float` alpha : `float` gamma : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` Returns: `float`
`StableDistributionFeller.XZCDF(x, alpha, gamma, aga)` Full Usage: `StableDistributionFeller.XZCDF(x, alpha, gamma, aga)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` Returns: `float`
`StableDistributionFeller.XZCDF(x, alpha, gamma, aga, tempStorage, precision)` Full Usage: `StableDistributionFeller.XZCDF(x, alpha, gamma, aga, tempStorage, precision)` Parameters: x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` gamma : `float` aga : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`