Distribution R¶

Domain for distributions formally given by moments. moments and different kinds of cumulants are stored in streams and computed on demand.

0: %

from DistributionCategory R

=: (%, %) -> Boolean

from BasicType

^: (%, PositiveInteger) -> %

from DistributionCategory R

~=: (%, %) -> Boolean

from BasicType

booleanConvolution: (%, %) -> %

from DistributionCategory R

booleanCumulant: (%, PositiveInteger) -> R

from DistributionCategory R

booleanCumulantFromJacobi: (Integer, Sequence R, Sequence R) -> R

booleanCumulantFromJacobi(n, aa, bb) computes the nth Boolean cumulant from the given Jacobiparameters aa and bb.

booleanCumulants: % -> Sequence R

from DistributionCategory R

classicalConvolution: (%, %) -> %

from DistributionCategory R

classicalCumulant: (%, PositiveInteger) -> R

from DistributionCategory R

classicalCumulants: % -> Sequence R

from DistributionCategory R

coerce: % -> OutputForm
construct: (Sequence R, Sequence R, Sequence R, Sequence R) -> %

construct(mom, ccum, fcum, bcum) constructs a distribution with moments mom, classical cumulants ccum, free cumulants fcum and boolean cumulants bcum. The user must make sure that these are consistent, otherwise the results are unpredictable!

distributionByBooleanCumulants: Sequence R -> %

distributionByBooleanCumulants(bb) initiates a distribution with given Boolean cumulants bb.

distributionByBooleanCumulants: Stream R -> %

distributionByBooleanCumulants(bb) initiates a distribution with given Boolean cumulants bb.

distributionByClassicalCumulants: Sequence R -> %

distributionByEvenMoments(kk) initiates a distribution with given classical cumulants kk.

distributionByClassicalCumulants: Stream R -> %

distributionByEvenMoments(kk) initiates a distribution with given classical cumulants kk.

distributionByEvenMoments: Sequence R -> %

distributionByEvenMoments(mm) initiates a distribution with given even moments mm and odd moments zero.

distributionByEvenMoments: Stream R -> %

distributionByEvenMoments(mm) initiates a distribution with given even moments mm and odd moments zero.

distributionByFreeCumulants: Sequence R -> %

distributionByFreeCumulants(cc) initiates a distribution with given free cumulants cc.

distributionByFreeCumulants: Stream R -> %

distributionByFreeCumulants(cc) initiates a distribution with given free cumulants cc.

distributionByJacobiParameters: (Sequence R, Sequence R) -> %

distributionByJacobiParameters(aa, bb) initiates a distribution with given Jacobi parameters [aa, bb].

distributionByJacobiParameters: (Stream R, Stream R) -> %

distributionByJacobiParameters(aa, bb) initiates a distribution with given Jacobi parameters [aa, bb].

distributionByMoments: Sequence R -> %

distributionByMoments(mm) initiates a distribution with given moments mm.

distributionByMoments: Stream R -> %

distributionByMoments(mm) initiates a distribution with given moments mm.

distributionByMonotoneCumulants: Sequence R -> % if R has Algebra Fraction Integer

distributionByMonotoneCumulants(hh) initiates a distribution with given monotone cumulants hh.

distributionByMonotoneCumulants: Stream R -> % if R has Algebra Fraction Integer

distributionByMonotoneCumulants(hh) initiates a distribution with given monotone cumulants hh.

distributionBySTransform: (Fraction Integer, Fraction Integer, Sequence R) -> % if R has Algebra Fraction Integer

distributionBySTransform(series) initiates a distribution with given S-transform series.

distributionBySTransform: Record(puiseux: Fraction Integer, laurent: Fraction Integer, coef: Sequence R) -> % if R has Algebra Fraction Integer

distributionBySTransform(series) initiates a distribution with given S-transform series.

freeConvolution: (%, %) -> %

from DistributionCategory R

freeCumulant: (%, PositiveInteger) -> R

from DistributionCategory R

freeCumulants: % -> Sequence R

from DistributionCategory R

freeMultiplicativeConvolution: (%, %) -> % if R has Algebra Fraction Integer

freeMultiplicativeConvolution(mu, nu) computes the free multiplicative convolution of the distributions mu and nu.

hankelDeterminants: % -> Stream R

from DistributionCategory R

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

jacobiParameters: % -> Record(an: Stream Fraction R, bn: Stream Fraction R) if R hasn’t Field and R has IntegralDomain

from DistributionCategory R

jacobiParameters: % -> Record(an: Stream R, bn: Stream R) if R has Field

from DistributionCategory R

latex: % -> String

from SetCategory

moment: (%, NonNegativeInteger) -> R

from DistributionCategory R

moments: % -> Sequence R

from DistributionCategory R

monotoneConvolution: (%, %) -> %

from DistributionCategory R

monotoneCumulants: % -> Sequence R if R has Algebra Fraction Integer

from DistributionCategory R

orthogonalConvolution: (%, %) -> %

from DistributionCategory R

orthogonalPolynomials: % -> Stream SparseUnivariatePolynomial Fraction R if R hasn’t Field and R has IntegralDomain

from DistributionCategory R

orthogonalPolynomials: % -> Stream SparseUnivariatePolynomial R if R has Field

from DistributionCategory R

subordinationConvolution: (%, %) -> %

from DistributionCategory R

BasicType

SetCategory