distributions with singularities in derivatives (e.g. Chi Squared with 3 degrees of freedom)

distributions with heavy tails (including Cauchy, Levy, Pareto)

distributions with no moments

Computations with two dependent random variables

Joint distributions: normal, copulas, joint distribution of two order statistics

Complicated operations on the two variables are possible, may involve additional intermediate variables

Operations on an arbitrary number of dependent variables in the style of Bayesian networks (initial implementation)

Limitations

Singularities at nonzero locations currently cause a loss of accuracy

Extremely heavy tails (e.g. decreasing as x**-1.1) cause a loss of accuracy

Computation time can be large for longer sequences of operations

Trigonometric functions are available but need improvements

Dependent variables come with some limitations

In the two variable case no singularities in p.d.f.'s are allowed and the result (but not the inputs) must have finite support

The Bayesian network based approach is limited to smooth densities with compact support and no singularities

Accuracy and efficiency may be lower than for independent variables

Currently special syntax is required to indicate dependencies should be taken into account

Sometimes it is possible to avoid computation on dependent
variables. For example let X=GammaDistr(5);
Y=GammaDistr(3). The expression X / (X+Y)
introduces a dependency between the numerator and denominator, but
after rewriting as 1 / (1+Y/X) the dependency disappears.
The results is the Beta distribution with parameters 5 and 3
computed with excellent accuracy.