MomentPackage(R)

distro.spad line 252 [edit on github]

An auxiliary package for various moment and cumulant transformations used in Distribution.

booleanCumulant2moment : Sequence(R) -> Sequence(R)

booleanCumulant2moment(cc) computes the sequence of moments from the sequence of boolean cumulants cc

cumulant2moment : Sequence(R) -> Sequence(R)

cumulant2moment(cc) computes the sequence of moments from the sequence of classical cumulants cc

freeCumulant2moment : Sequence(R) -> Sequence(R)

freeCumulant2moment(cc) computes the sequence of moments from the sequence of free cumulants cc

hankelDeterminant : (Sequence(R), NonNegativeInteger) -> R

hankelDeterminant(x, n) returns the nth Hankel determinant of the sequence x.

jacobi2poly : (Stream(R), Stream(R)) -> Stream(SparseUnivariatePolynomial(R))

jacobi2poly(aa, bb) returns the stream of orthogonal polynomials corresponding to the Jacobi parameters a_n and b_n.

moment2Stransform : Sequence(R) -> Record(puiseux : Fraction(Integer), laurent : Fraction(Integer), coef : Sequence(R)) if R has Algebra(Fraction(Integer))

moment2Stransform(x) returns the Puiseux and Laurent order and coefficients of the S transform of x

moment2booleanCumulant : Sequence(R) -> Sequence(R)

moment2booleanCumulant(mm) computes the sequence of boolean cumulants from the sequence of moments mm

moment2cumulant : Sequence(R) -> Sequence(R)

moment2cumulant(mm) computes the sequence of classical cumulants from the sequence of moments mm

moment2freeCumulant : Sequence(R) -> Sequence(R)

moment2freeCumulant(mm) computes the sequence of free cumulants from the sequence of moments mm

moment2jacobi : Sequence(R) -> Record(an : Stream(R), bn : Stream(R)) if R has Field

moment2jacobi(mm) computes the Jacobi parameters as pair of streams.

moment2jacobi2 : Sequence(R) -> Stream(Record(an : R, bn : R)) if R has Field

moment2jacobi2(mm) computes the Jacobi parameters as stream of pairs $(an, bn)$.

moment2monotoneCumulant : Sequence(R) -> Sequence(R)

moment2monotoneCumulant(mm) computes the sequence of monotone cumulants from the sequence of moments mm

moment2nthJacobi : List(R) -> Record(an : List(R), bn : List(R)) if R has Field

moment2nthJacobi(mm) computes the list of Jacobi parameters from the list of moments mm as far as possible.

monotoneCumulant2moment : Sequence(R) -> Sequence(R)

monotoneCumulant2moment(hh) computes the sequence of moments from the sequence of monotone cumulants hh

monotoneCumulant2momentPoly : Sequence(R) -> Sequence(SparseUnivariatePolynomial(R))

monotoneCumulant2momentPoly(hh) computes the sequence of moment polynomials $m_n(t)$ from the sequence of monotone cumulants hh