Distribution(R)

distro.spad line 694 [edit on github]

• R : CommutativeRing

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)

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)

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

from DistributionCategory(R)

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

from DistributionCategory(R)

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

from DistributionCategory(R)

subordinationConvolution : (%, %) -> %

from DistributionCategory(R)

~= : (%, %) -> Boolean

from BasicType

BasicType

SetCategory

DistributionCategory(R)

CoercibleTo(OutputForm)