DistributionPolynomialPackage(R, S, UPS)

distro.spad line 1015 [edit on github]

• R : CommutativeRing
• S : Join(CommutativeRing, Module(R))
• UPS : UnivariatePolynomialCategory(S)

A package to apply polynomial transformations to distributions and integrate polynomials with respect to distributions.

apply : (UPS, Distribution(R)) -> Distribution(S)

apply(p, d) computes the distribution of the random variable p(X)$ where X has distribution d.

eval : (Distribution(R), UPS) -> S

eval(d, p) evaluates the distribution d as a linear functional on the polynomial p. Same as integrate(p, d).

integrate : (UPS, Distribution(R)) -> S

integrate(p, d) integrates the polynomial p against the distribution d. Same as eval(d, p).