StableDistributionSymmetric (FsODE)

FsODE

Documentation for 0.0.2

StableDistributionSymmetric Type

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

Represents a symmetric stable distribution in Zolotarev's parametrization.

References:

[1] Matsui M., Takemura A.: "Some Improvements in Numerical Evaluation of Symmetric Stable Densities and its Derivatives", Discussion Paper, CIRJE-F-292, Tokio, August 2004

Constructors

Constructor	Description
`StableDistributionSymmetric(gen)` Full Usage: `StableDistributionSymmetric(gen)` Parameters: gen : `Generator`	gen : `Generator`

Static members

Static member	Description
`StableDistributionSymmetric.CCDF(x, alpha)` Full Usage: `StableDistributionSymmetric.CCDF(x, alpha)` Parameters: x : `float` alpha : `float` Returns: `float`	x : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.CCDF(x, alpha, tempStorage, precision)` Full Usage: `StableDistributionSymmetric.CCDF(x, alpha, tempStorage, precision)` Parameters: x : `float` alpha : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionSymmetric.CDF(x, alpha)` Full Usage: `StableDistributionSymmetric.CDF(x, alpha)` Parameters: x : `float` alpha : `float` Returns: `float`	x : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.CDF(x, alpha, tempStorage, precision)` Full Usage: `StableDistributionSymmetric.CDF(x, alpha, tempStorage, precision)` Parameters: x : `float` alpha : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`
`StableDistributionSymmetric.GetAgt1GnParameter(x, alpha, factorp, factorw, dev, logPrefactor)` Full Usage: `StableDistributionSymmetric.GetAgt1GnParameter(x, alpha, factorp, factorw, dev, logPrefactor)` Parameters: x : `float` alpha : `float` factorp : `byref<float>` factorw : `byref<float>` dev : `byref<float>` logPrefactor : `byref<float>`	x : `float` alpha : `float` factorp : `byref<float>` factorw : `byref<float>` dev : `byref<float>` logPrefactor : `byref<float>`
`StableDistributionSymmetric.GetAlt1GnParameter(x, alpha, factorp, facdiv, dev, logPdfPrefactor)` Full Usage: `StableDistributionSymmetric.GetAlt1GnParameter(x, alpha, factorp, facdiv, dev, logPdfPrefactor)` Parameters: x : `float` alpha : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`	x : `float` alpha : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`
`StableDistributionSymmetric.GetAlt1GpParameterByGamma(x, alpha, factorp, facdiv, dev, logPdfPrefactor)` Full Usage: `StableDistributionSymmetric.GetAlt1GpParameterByGamma(x, alpha, factorp, facdiv, dev, logPdfPrefactor)` Parameters: x : `float` alpha : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`	x : `float` alpha : `float` factorp : `byref<float>` facdiv : `byref<float>` dev : `byref<float>` logPdfPrefactor : `byref<float>`
`StableDistributionSymmetric.PDF(x, alpha)` Full Usage: `StableDistributionSymmetric.PDF(x, alpha)` Parameters: x : `float` alpha : `float` Returns: `float`	x : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.PDF(x, alpha, tempStorage, precision)` Full Usage: `StableDistributionSymmetric.PDF(x, alpha, tempStorage, precision)` Parameters: x : `float` - The argument. alpha : `float` - tempStorage : `byref<obj>` - Object which can be used to speed up subsequent calculations of the function. At the first call, provide an object initialized with and provide this object for the following calculations. precision : `float` - Goal for the relative precision. 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` tempStorage : `byref<obj>` Object which can be used to speed up subsequent calculations of the function. At the first call, provide an object initialized with and provide this object for the following calculations. precision : `float` Goal for the relative precision. Returns: `float`
`StableDistributionSymmetric.PDFAlphaBetween01And02(x, alpha, precision, tempStorage)` Full Usage: `StableDistributionSymmetric.PDFAlphaBetween01And02(x, alpha, precision, tempStorage)` Parameters: x : `float` - alpha : `float` - precision : `float` - tempStorage : `byref<obj>` - 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` precision : `float` tempStorage : `byref<obj>` Returns: `float`
`StableDistributionSymmetric.PDFAlphaBetween02And099(x, alpha, precision, tempStorage)` Full Usage: `StableDistributionSymmetric.PDFAlphaBetween02And099(x, alpha, precision, tempStorage)` Parameters: x : `float` - alpha : `float` - precision : `float` - tempStorage : `byref<obj>` - 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` precision : `float` tempStorage : `byref<obj>` Returns: `float`
`StableDistributionSymmetric.PDFAlphaBetween099And101(x, alpha, precision, tempStorage)` Full Usage: `StableDistributionSymmetric.PDFAlphaBetween099And101(x, alpha, precision, tempStorage)` Parameters: x : `float` - alpha : `float` - precision : `float` - tempStorage : `byref<obj>` - Returns: `float`	Calculation of the PDF if alpha is inbetween 0.99 and 1.01. x : `float` alpha : `float` precision : `float` tempStorage : `byref<obj>` Returns: `float`
`StableDistributionSymmetric.PDFAlphaBetween101And199999(x, alpha, precision, tempStorage)` Full Usage: `StableDistributionSymmetric.PDFAlphaBetween101And199999(x, alpha, precision, tempStorage)` Parameters: x : `float` - alpha : `float` - precision : `float` - tempStorage : `byref<obj>` - 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` precision : `float` tempStorage : `byref<obj>` Returns: `float`
`StableDistributionSymmetric.PDFAlphaBetween199999And2(x, alpha, precision, tempStorage)` Full Usage: `StableDistributionSymmetric.PDFAlphaBetween199999And2(x, alpha, precision, tempStorage)` Parameters: x : `float` - alpha : `float` - precision : `float` - tempStorage : `byref<obj>` - 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` precision : `float` tempStorage : `byref<obj>` Returns: `float`
`StableDistributionSymmetric.PDFIntegration(x, alpha, precision, tempStorage)` Full Usage: `StableDistributionSymmetric.PDFIntegration(x, alpha, precision, tempStorage)` Parameters: x : `float` alpha : `float` precision : `float` tempStorage : `byref<obj>` Returns: `float`	x : `float` alpha : `float` precision : `float` tempStorage : `byref<obj>` Returns: `float`
`StableDistributionSymmetric.PDFSeriesBigX(z, alpha)` Full Usage: `StableDistributionSymmetric.PDFSeriesBigX(z, alpha)` Parameters: z : `float` - Circular frequency. alpha : `float` - Alpha (broadness) parameter. 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 high 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` Alpha (broadness) parameter. Returns: `float` Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies, or double.NaN if the series not converges.
`StableDistributionSymmetric.PDFSeriesSmallX(z, alpha)` Full Usage: `StableDistributionSymmetric.PDFSeriesSmallX(z, alpha)` Parameters: z : `float` - Circular frequency. alpha : `float` - Beta parameter. 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 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. 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 high frequencies, or double.NaN if the series not converges.
`StableDistributionSymmetric.PDFSeriesSmallXSmallAlpha(z, alpha)` Full Usage: `StableDistributionSymmetric.PDFSeriesSmallXSmallAlpha(z, alpha)` Parameters: z : `float` - Circular frequency. alpha : `float` - Alpha (broadness) parameter. Returns: `float` Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies, or double.NaN if the series not converges.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, and beta<=1/20.. 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` Alpha (broadness) parameter. Returns: `float` Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies, or double.NaN if the series not converges.Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies, or double.NaN if the series not converges.
`StableDistributionSymmetric.PDFTaylorExpansionAroundAlphaOne(x, alpha)` Full Usage: `StableDistributionSymmetric.PDFTaylorExpansionAroundAlphaOne(x, alpha)` Parameters: x : `float` alpha : `float` Returns: `float`	x : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.Quantile(p, alpha)` Full Usage: `StableDistributionSymmetric.Quantile(p, alpha)` Parameters: p : `float` alpha : `float` Returns: `float`	p : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.QuantileCCDF(q, alpha)` Full Usage: `StableDistributionSymmetric.QuantileCCDF(q, alpha)` Parameters: q : `float` alpha : `float` Returns: `float`	q : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.XZCDF(x, alpha)` Full Usage: `StableDistributionSymmetric.XZCDF(x, alpha)` Parameters: x : `float` alpha : `float` Returns: `float`	x : `float` alpha : `float` Returns: `float`
`StableDistributionSymmetric.XZCDF(x, alpha, tempStorage, precision)` Full Usage: `StableDistributionSymmetric.XZCDF(x, alpha, tempStorage, precision)` Parameters: x : `float` alpha : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`	x : `float` alpha : `float` tempStorage : `byref<obj>` precision : `float` Returns: `float`