Table 2 Random variables and their polynomials

From: Full-cycle prediction of crack healing in self-healing concrete using generalized polynomial chaos expansion

 

Random variables (ξ)

Wiener-Askey chaos {ψ(ξ)}

Support

Continuous

Gaussian

Hermite-chaos

(-∞, ∞)

Gamma

Laguerre-chaos

[0, ∞)

Beta

Jacobi-chaos

[a, b]

Uniform

Legendre-chaos

[a, b]

Discrete

Poisson

Charlier-chaos

[1 … …]

Binomial

Krawtchouk-chaos

{0, 1,…,N}

Negative binomial

Meixner-chaos

{0, 1, 2, …}

Hypergeometric

Hahn-chaos

{0, 1,…,N}

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