Different nondeterministic methods have differing support for
uncertain variable distributions. Tables \ref T5d37 "5.37", \ref 
T5d38 "5.38", and \ref T5d39 "5.39" 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 \c active \c 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 \ref method-polynomial_chaos and \ref
  method-stoch_collocation for additional information on these three
  options.
- methods supporting the epistemic interval distributions have differing
  approaches: \c sampling and the \c lhs option of \c 
  global_interval_est model the interval basic probability
  assignments (BPAs) as continuous histogram bin distributions for
  purposes of generating samples; \c local_interval_est and the 
  \c ego option of \c global_interval_est ignore the BPA details 
  and models these variables as simple bounded regions defined by the 
  cell extremes; and \c local_evidence and \c global_evidence
  model the interval specifications as true BPAs.

<!-- could go into more detail on sub-options of local/global evidence, 
     but I think that's probably overkill. -->
<!-- and a "C#" denotes that correlations are only supported between 
variables of this type and other variables in the same numbered set. -->

\anchor T5d37
<table>
<caption align = "top">
\htmlonly
Table 5.37
\endhtmlonly
Summary of Distribution Types supported by Nondeterministic Methods, Part I (Continuous Aleatory Types)
</caption>
<tr>
<td><b>Distribution Type</b>
<td><b>Sampling</b>
<td><b>Local Reliability</b>
<td><b>Global Reliability</b>
<td><b>Wiener SE</b>
<td><b>Askey SE</b>
<td><b>Extended SE</b>
<td><b>Piecewise SE</b>
<td><b>Local Interval</b>
<td><b>Global Interval</b>
<td><b>Local Evidence</b>
<td><b>Global Evidence</b>
<tr>
<td>Normal
<td>C
<td>C
<td>C
<td>C
<td>C
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Bounded Normal
<td>C
<td>U
<td>U
<td>U
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Lognormal
<td>C
<td>C
<td>C
<td>C
<td>C
<td>U
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Bounded Lognormal
<td>C
<td>U
<td>U
<td>U
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Uniform
<td>C
<td>C
<td>C
<td>C
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Loguniform
<td>C
<td>U
<td>U
<td>U
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Triangular
<td>C
<td>U
<td>U
<td>U
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Exponential
<td>C
<td>C
<td>C
<td>C
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Beta
<td>C
<td>U
<td>U
<td>U
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Gamma
<td>C
<td>C
<td>C
<td>C
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Gumbel
<td>C
<td>C
<td>C
<td>C
<td>C
<td>U
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Frechet
<td>C
<td>C
<td>C
<td>C
<td>C
<td>U
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Weibull
<td>C
<td>C
<td>C
<td>C
<td>C
<td>U
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Continuous Histogram Bin
<td>C
<td>U
<td>U
<td>U
<td>U
<td>U
<td>U
<td>-
<td>-
<td>-
<td>-
</table>  

\anchor T5d38
<table>
<caption align = "top">
\htmlonly
Table 5.38
\endhtmlonly
Summary of Distribution Types supported by Nondeterministic Methods, Part II (Discrete Aleatory Types)
</caption>
<tr>
<td><b>Distribution Type</b>
<td><b>Sampling</b>
<td><b>Local Reliability</b>
<td><b>Global Reliability</b>
<td><b>Wiener SE</b>
<td><b>Askey SE</b>
<td><b>Extended SE</b>
<td><b>Piecewise SE</b>
<td><b>Local Interval</b>
<td><b>Global Interval</b>
<td><b>Local Evidence</b>
<td><b>Global Evidence</b>
<tr>
<td>Poisson
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Binomial
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Negative Binomial
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Geometric
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Hypergeometric
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Discrete Histogram Point
<td>C
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
</table>

\anchor T5d39
<table>
<caption align = "top">
\htmlonly
Table 5.39
\endhtmlonly
Summary of Distribution Types supported by Nondeterministic Methods, Part III (Epistemic, Design, and State Types)
</caption>
<tr>
<td><b>Distribution Type</b>
<td><b>Sampling</b>
<td><b>Local Reliability</b>
<td><b>Global Reliability</b>
<td><b>Wiener SE</b>
<td><b>Askey SE</b>
<td><b>Extended SE</b>
<td><b>Piecewise SE</b>
<td><b>Local Interval</b>
<td><b>Global Interval</b>
<td><b>Local Evidence</b>
<td><b>Global Evidence</b>
<tr>
<td>Interval
<td>U
<td>-
<td>U,A
<td>U,A
<td>U,A
<td>U,A
<td>U,A
<td>U
<td>U
<td>U
<td>U
<tr>
<td>Continuous Design
<td>U,A
<td>-
<td>U,A
<td>U,A
<td>U,A
<td>U,A
<td>U,A
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Discrete Design Range, Int Set, Real Set
<td>U,A
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Continuous State
<td>U,A
<td>-
<td>U,A
<td>U,A
<td>U,A
<td>U,A
<td>U,A
<td>-
<td>-
<td>-
<td>-
<tr>
<td>Discrete State Range, Int Set, Real Set
<td>U,A
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
<td>-
</table>  
