Distribution RΒΆ

distro.spad line 1123

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

BasicType

CoercibleTo OutputForm

DistributionCategory R

SetCategory