MomentPackage RΒΆ

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 `n`th 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`