# DistributionCategory R¶

Category of distributions formally given by moments.

0: %
0 is the Dirac distribution
=: (%, %) -> Boolean
from BasicType
^: (%, PositiveInteger) -> %
x^k constructs the distribution of the kth power of the random variable with distribution X by picking every k-th moment.
~=: (%, %) -> Boolean
from BasicType
booleanConvolution: (%, %) -> %
booleanConvolution(x, y) returns the boolean convolution of the distributions x and y
booleanCumulant: (%, PositiveInteger) -> R
booleanCumulant(x, n) returns the n-th boolean cumulant of the distribution x
booleanCumulants: % -> Sequence R
booleanCumulants(x) returns the sequence of boolean cumulants of the distribution x.
classicalConvolution: (%, %) -> %
classicalConvolution(x, y) returns the classical convolution of the distributions x and y
classicalCumulant: (%, PositiveInteger) -> R
classicalCumulant(x, n) returns the n-th classical cumulant of the distribution x
classicalCumulants: % -> Sequence R
classicalCumulants(x) returns sequence of classical cumulants of the distribution x
coerce: % -> OutputForm
from CoercibleTo OutputForm
freeConvolution: (%, %) -> %
freeConvolution(x, y) returns the free convolution of the distributions x and y
freeCumulant: (%, PositiveInteger) -> R
freeCumulant(x, n) returns the n-th free cumulant of the distribution x
freeCumulants: % -> Sequence R
freeCumulants(x) returns the sequence of free cumulants of the distribution x.
hankelDeterminants: % -> Stream R
hankelDeterminants(x) returns the stream of hankel determinants of the distribution x.
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
jacobiParameters(x) returns the pair of streams of Jacobi parameters of the distribution x.
jacobiParameters: % -> Record(an: Stream R, bn: Stream R) if R has Field
jacobiParameters(x) returns the pair of streams of Jacobi parameters of the distribution x.
latex: % -> String
from SetCategory
moment: (%, NonNegativeInteger) -> R
moment(x, n) returns the n-th moment of the distribution x
moments: % -> Sequence R
moments(x) returns the sequence of moments of the distribution x
monotoneConvolution: (%, %) -> %
monotoneConvolution(x, y) returns the monotone convolution of the distributions x and y
monotoneCumulants: % -> Sequence R if R has Algebra Fraction Integer
monotoneCumulants(x) returns the sequence of monotone cumulants of the distribution x.
orthogonalPolynomials: % -> Stream SparseUnivariatePolynomial Fraction R if R has IntegralDomain and R hasn’t Field
orthogonalPolynomials(x) returns the stream of orthogonal polynomials.
orthogonalPolynomials: % -> Stream SparseUnivariatePolynomial R if R has Field
orthogonalPolynomials(x) returns the stream of orthogonal polynomials.

BasicType

SetCategory