MomentPackage R¶

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.

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

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

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

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

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

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.

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

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