# Variable Support

Different nondeterministic methods have differing support for
uncertain variable distributions. Table 13,
Table 14, and Table 15
summarize the uncertain variables that are available for use by the different methods, where a “-”
indicates that the distribution is not supported by the method, a “U”
means the uncertain input variables of this type must be uncorrelated,
a “C” denotes that correlations are supported involving uncertain
input variables of this type, and an “A” means the appropriate
variables must be specified as active in the variables
specification block. For example, if one wants to support
sampling or a stochastic expansion method over both
continuous uncertain and continuous state variables, the
specification `active all`

must be listed in the variables
specification block.
Additional notes include:

we have four variants for stochastic expansions (SE), listed as Wiener, Askey, Extended, and Piecewise which draw from different sets of basis polynomials. The term stochastic expansion indicates polynomial chaos and stochastic collocation collectively, although the Piecewise option is only currently supported for stochastic collocation. Refer to

`polynomial_chaos`

and`stoch_collocation`

for additional information on these three options.methods supporting the epistemic interval distributions have differing approaches:

`sampling`

and`global_interval_est lhs`

model the interval basic probability assignments (BPAs) as continuous histogram bin distributions for purposes of generating samples;`local_interval_est`

and`global_interval_est ego`

ignore the BPA details and models these variables as simple bounded regions defined by the cell extremes;and

`local_evidence`

and`global_evidence`

model the interval specifications as true BPAs.

Distribution Type |
Sampling |
Local Reliability |
Global Reliability |
Wiener SE |
Askey SE |
Extended SE |
Piecewise SE |
Local Interval |
Global Interval |
Local Evidence |
Global Evidence |
---|---|---|---|---|---|---|---|---|---|---|---|

Normal |
C |
C |
C |
C |
C |
C |
- |
- |
- |
- |
- |

Bounded Normal |
C |
U |
U |
U |
U |
U |
U |
- |
- |
- |
- |

Lognormal |
C |
C |
C |
C |
C |
U |
- |
- |
- |
- |
- |

Bounded Lognormal |
C |
U |
U |
U |
U |
U |
U |
- |
- |
- |
- |

Uniform |
C |
C |
C |
C |
U |
U |
U |
- |
- |
- |
- |

Loguniform |
C |
U |
U |
U |
U |
U |
U |
- |
- |
- |
- |

Triangular |
C |
U |
U |
U |
U |
U |
U |
- |
- |
- |
- |

Exponential |
C |
C |
C |
C |
U |
U |
- |
- |
- |
- |
- |

Beta |
C |
U |
U |
U |
U |
U |
U |
- |
- |
- |
- |

Gamma |
C |
C |
C |
C |
U |
U |
- |
- |
- |
- |
- |

Gumbel |
C |
C |
C |
C |
C |
U |
- |
- |
- |
- |
- |

Frechet |
C |
C |
C |
C |
C |
U |
- |
- |
- |
- |
- |

Weibull |
C |
C |
C |
C |
C |
U |
- |
- |
- |
- |
- |

Continuous Histogram Bin |
C |
U |
U |
U |
U |
U |
U |
- |
- |
- |
- |

Distribution Type |
Sampling |
Local Reliability |
Global Reliability |
Wiener SE |
Askey SE |
Extended SE |
Piecewise SE |
Local Interval |
Global Interval |
Local Evidence |
Global Evidence |
---|---|---|---|---|---|---|---|---|---|---|---|

Poisson |
C |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Binomial |
C |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Negative Binomial |
C |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Geometric |
C |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Hypergeometric |
C |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Discrete Histogram Point |
C |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Distribution Type |
Sampling |
Local Reliability |
Global Reliability |
Wiener SE |
Askey SE |
Extended SE |
Piecewise SE |
Local Interval |
Global Interval |
Local Evidence |
Global Evidence |
---|---|---|---|---|---|---|---|---|---|---|---|

Interval |
U |
- |
U,A |
U,A |
U,A |
U,A |
U,A |
U |
U |
U |
U |

Continuous Design |
U,A |
- |
U,A |
U,A |
U,A |
U,A |
U,A |
- |
- |
- |
- |

Discrete Design Range, Int Set, Real Set |
U,A |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |

Continuous State |
U,A |
- |
U,A |
U,A |
U,A |
U,A |
U,A |
- |
- |
- |
- |

Discrete State Range, Int Set, Real Set |
U,A |
- |
- |
- |
- |
- |
- |
- |
- |
- |
- |