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
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 hasn’t Field and R has IntegralDomain

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.

orthogonalConvolution: (%, %) -> %

orthogonalConvolution(x, y) returns the orthogonal convolution of the distributions x and y

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

orthogonalPolynomials(x) returns the stream of orthogonal polynomials.

orthogonalPolynomials: % -> Stream SparseUnivariatePolynomial R if R has Field

orthogonalPolynomials(x) returns the stream of orthogonal polynomials.

subordinationConvolution: (%, %) -> %

subordinationConvolution(x, y) returns the subordination convolution of the distributions x and y

BasicType

SetCategory