.. _method-stoch_collocation-askey:

"""""
askey
"""""


Select the standardized random variables (and associated basis polynomials) from the Askey family that best match the user-specified random variables.


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**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* extended (Askey + numerically-generated)


**Description**


The Askey option employs standard normal, standard
uniform, standard exponential, standard beta, and standard gamma
random variables in a transformed probability space.  These selections
correspond to Hermite, Legendre, Laguerre, Jacobi, and generalized
Laguerre orthogonal polynomials, respectively.

Specific mappings for the basis polynomials are based on a closest
match criterion, and include Hermite for normal (optimal) as well as
bounded normal, lognormal, bounded lognormal, gumbel, frechet, and
weibull (sub-optimal); Legendre for uniform (optimal) as well as
loguniform, triangular, and bin-based histogram (sub-optimal);
Laguerre for exponential (optimal); Jacobi for beta (optimal); and
generalized Laguerre for gamma (optimal).