StableDistributionBase (FsODE)

FsODE

Documentation for 0.0.2

StableDistributionBase Type

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

Represents the base of all StableDistributions classes in different parametrizations.

Constructors

Constructor	Description
`StableDistributionBase(generator)` Full Usage: `StableDistributionBase(generator)` Parameters: generator : `Generator` - The random number generator used.	Initializes a new instance of the StableDistributionBase class. generator : `Generator` The random number generator used.

Instance members

Instance member	Description
`this.Maximum` Full Usage: `this.Maximum` Returns: `float` Modifiers: abstract	Gets the maximum possible value of distributed random numbers. Returns: `float`
`this.Mean` Full Usage: `this.Mean` Returns: `float` Modifiers: abstract	Gets the mean of distributed random numbers. Returns: `float`
`this.Median` Full Usage: `this.Median` Returns: `float` Modifiers: abstract	Gets the median of distributed random numbers. Returns: `float`
`this.Minimum` Full Usage: `this.Minimum` Returns: `float` Modifiers: abstract	Gets the minimum possible value of distributed random numbers. Returns: `float`
`this.Mode` Full Usage: `this.Mode` Returns: `float[]` Modifiers: abstract	Gets the mode of distributed random numbers. Returns: `float[]`
`this.NextDouble` Full Usage: `this.NextDouble` Returns: `float` A distributed double-precision floating point number. Modifiers: abstract	Returns a distributed floating point random number. Returns: `float` A distributed double-precision floating point number.
`this.Variance` Full Usage: `this.Variance` Returns: `float` Modifiers: abstract	Gets the variance of distributed random numbers. Returns: `float`

Static members

Static member	Description
`StableDistributionBase.BetaFromAlphaGammaAga(alpha, gamma, aga, abe)` Full Usage: `StableDistributionBase.BetaFromAlphaGammaAga(alpha, gamma, aga, abe)` Parameters: alpha : `float` gamma : `float` aga : `float` abe : `byref<float>` Returns: `float`	alpha : `float` gamma : `float` aga : `float` abe : `byref<float>` Returns: `float`
`StableDistributionBase.BracketRootByExtensionOnly(func, ysearch, x0, x1)` Full Usage: `StableDistributionBase.BracketRootByExtensionOnly(func, ysearch, x0, x1)` Parameters: func : `Func<float, float>` - The function used to evaluate the function values. ysearch : `float` - The value to find. x0 : `byref<float>` - Starting parameter of x0, at the end the lower value of the bracket interval. x1 : `byref<float>` - Starting parameter of x1, at the end the upper value of the bracket interval. Returns: `bool` True if a bracket interval was found. If such an interval could not be found, the return value is false.	Find the bracket of a root, i.e. values for x0 and x1, so that ysearch is inbetween f(x0) and f(x1). This is done be extension of the interval [x0,x1] either to the left or the right side or both. `True` is returned when a bracket was found. func : `Func<float, float>` The function used to evaluate the function values. ysearch : `float` The value to find. x0 : `byref<float>` Starting parameter of x0, at the end the lower value of the bracket interval. x1 : `byref<float>` Starting parameter of x1, at the end the upper value of the bracket interval. Returns: `bool` True if a bracket interval was found. If such an interval could not be found, the return value is false.
`StableDistributionBase.CosXPiBy2(x)` Full Usage: `StableDistributionBase.CosXPiBy2(x)` Parameters: x : `float` - Argument x. Returns: `float` Cos(x*Pi/2) with high accuracy.	Calculates the cosine of x times Pi/2 with increased accuracy. x : `float` Argument x. Returns: `float` Cos(x*Pi/2) with high accuracy.
`StableDistributionBase.GetAbeFromBeta(beta)` Full Usage: `StableDistributionBase.GetAbeFromBeta(beta)` Parameters: beta : `float` - The beta value. Returns: `float` If beta is >= 0, the return value is (1-beta). Else, if beta is <0, the return value is (1+beta).	Calculates the 'alternative beta' value abe from the skewness parameter beta. The value abe helps to specifiy beta with enhanced accuracy especially when \|beta\| is close to 1. Of course, this helper function is only intended to give a correct abe value for a given beta. But in order to specify beta with enhanced accuracy around \|beta\|=1, you should specify abe first, and then calculate beta from abe, which can be done with StableDistributionBase.GetBetaFromAbe. beta : `float` The beta value. Returns: `float` If beta is >= 0, the return value is (1-beta). Else, if beta is <0, the return value is (1+beta).
`StableDistributionBase.GetBetaFromAbe(abe, isBetaNegative)` Full Usage: `StableDistributionBase.GetBetaFromAbe(abe, isBetaNegative)` Parameters: abe : `float` - 'Alternative beta' value. It is defined as (1-beta) for beta>=0, and as (1+beta) for beta<0. Thus, abe is a value in the range [0,1]. isBetaNegative : `bool` - Specifies the sign of the original beta value. If false, the original beta is a nonnegative value. Of true, the original beta is negative. Returns: `float` The skewness parameter beta (range: [-1,1]) as calculated from the 'alternative beta' value abe.	Gets the skewness parameter beta (range: [-1,1]) from the 'alternative beta' value abe. abe : `float` 'Alternative beta' value. It is defined as (1-beta) for beta>=0, and as (1+beta) for beta<0. Thus, abe is a value in the range [0,1]. isBetaNegative : `bool` Specifies the sign of the original beta value. If false, the original beta is a nonnegative value. Of true, the original beta is negative. Returns: `float` The skewness parameter beta (range: [-1,1]) as calculated from the 'alternative beta' value abe.
`StableDistributionBase.OneMinusExp(x)` Full Usage: `StableDistributionBase.OneMinusExp(x)` Parameters: x : `float` - Function argument Returns: `float` 1-Exp(x)	Calculates 1-Exp(x) with more accuracy around x=0. If \|x\| is smaller than StableDistributionBase.OneMinusExp_SmallBound, the series expansion of (1-Exp(x)) is used for calculation. If \|x\| is greater than or equal to StableDistributionBase.OneMinusExp_SmallBound, the standard way of evaluation is used. x : `float` Function argument Returns: `float` 1-Exp(x)
`StableDistributionBase.ParameterConversionFellerToS0(alpha, gamma, aga, sigmaf, muf, beta, abe, sigma0, mu0)` Full Usage: `StableDistributionBase.ParameterConversionFellerToS0(alpha, gamma, aga, sigmaf, muf, beta, abe, sigma0, mu0)` Parameters: alpha : `float` gamma : `float` aga : `float` sigmaf : `float` muf : `float` beta : `byref<float>` abe : `byref<float>` sigma0 : `byref<float>` mu0 : `byref<float>`	alpha : `float` gamma : `float` aga : `float` sigmaf : `float` muf : `float` beta : `byref<float>` abe : `byref<float>` sigma0 : `byref<float>` mu0 : `byref<float>`
`StableDistributionBase.ParameterConversionFellerToS1(alpha, gamma, aga, sigmaf, muf, beta, abe, sigma1, mu1)` Full Usage: `StableDistributionBase.ParameterConversionFellerToS1(alpha, gamma, aga, sigmaf, muf, beta, abe, sigma1, mu1)` Parameters: alpha : `float` gamma : `float` aga : `float` sigmaf : `float` muf : `float` beta : `byref<float>` abe : `byref<float>` sigma1 : `byref<float>` mu1 : `byref<float>`	alpha : `float` gamma : `float` aga : `float` sigmaf : `float` muf : `float` beta : `byref<float>` abe : `byref<float>` sigma1 : `byref<float>` mu1 : `byref<float>`
`StableDistributionBase.ParameterConversionS0ToFeller(alpha, beta, abe, sigma0, mu0, gamma, aga, sigmaf, muf)` Full Usage: `StableDistributionBase.ParameterConversionS0ToFeller(alpha, beta, abe, sigma0, mu0, gamma, aga, sigmaf, muf)` Parameters: alpha : `float` beta : `float` abe : `float` sigma0 : `float` mu0 : `float` gamma : `byref<float>` aga : `byref<float>` sigmaf : `byref<float>` muf : `byref<float>`	alpha : `float` beta : `float` abe : `float` sigma0 : `float` mu0 : `float` gamma : `byref<float>` aga : `byref<float>` sigmaf : `byref<float>` muf : `byref<float>`
`StableDistributionBase.ParameterConversionS0ToS1(alpha, beta, sigma0, mu0, mu1)` Full Usage: `StableDistributionBase.ParameterConversionS0ToS1(alpha, beta, sigma0, mu0, mu1)` Parameters: alpha : `float` beta : `float` sigma0 : `float` mu0 : `float` mu1 : `byref<float>`	alpha : `float` beta : `float` sigma0 : `float` mu0 : `float` mu1 : `byref<float>`
`StableDistributionBase.ParameterConversionS1ToFeller(alpha, beta, abe, sigma1, mu1, gamma, aga, sigmaf, muf)` Full Usage: `StableDistributionBase.ParameterConversionS1ToFeller(alpha, beta, abe, sigma1, mu1, gamma, aga, sigmaf, muf)` Parameters: alpha : `float` beta : `float` abe : `float` sigma1 : `float` mu1 : `float` gamma : `byref<float>` aga : `byref<float>` sigmaf : `byref<float>` muf : `byref<float>`	alpha : `float` beta : `float` abe : `float` sigma1 : `float` mu1 : `float` gamma : `byref<float>` aga : `byref<float>` sigmaf : `byref<float>` muf : `byref<float>`
`StableDistributionBase.ParameterConversionS1ToS0(alpha, beta, sigma1, mu1, mu0)` Full Usage: `StableDistributionBase.ParameterConversionS1ToS0(alpha, beta, sigma1, mu1, mu0)` Parameters: alpha : `float` beta : `float` sigma1 : `float` mu1 : `float` mu0 : `byref<float>`	alpha : `float` beta : `float` sigma1 : `float` mu1 : `float` mu0 : `byref<float>`
`StableDistributionBase.PowerOfOnePlusXSquared(x, pow)` Full Usage: `StableDistributionBase.PowerOfOnePlusXSquared(x, pow)` Parameters: x : `float` - Argument x. pow : `float` - Power. Returns: `float` The value (1+x²)^pow with increased accuary.	Calculates (1+x²)^pow with increased accuracy, for both small and big values of \|x\|. x : `float` Argument x. pow : `float` Power. Returns: `float` The value (1+x²)^pow with increased accuary.
`StableDistributionBase.SinXPiBy2(x)` Full Usage: `StableDistributionBase.SinXPiBy2(x)` Parameters: x : `float` - Argument x. Returns: `float` Sin(x*Pi/2) with high accuracy.	Calculates the sine of x times Pi/2 with increased accuracy. x : `float` Argument x. Returns: `float` Sin(x*Pi/2) with high accuracy.