# Graph a ParameterMixtureDistribution

I am trying to graph the following 'ParameterMixtureDistribution'.

pmd = ParameterMixtureDistribution[
v], {m \[Distributed]
UniformDistribution[{0.00000001, 0.2}],
v \[Distributed] UniformDistribution[{0.00000001, 0.2}]}]


I would know if PDF[pmd] were to return something but it does not. Is there a way I can graph my complex distribution?

I think you should report this to support. I'm not sure if this can be classified as a bug, but this takes way longer than it's supposed to, even after replacing the inexact 0.00000001 and 0.2 with the equivalents 1*^-8 and 1/5.

In the meantime, here is a very hack-y method for (relatively quickly) evaluating the PDF of your distribution:

pmd = ParameterMixtureDistribution[GammaDistribution[m/v, m^2/v],
{m \[Distributed] UniformDistribution[{1*^-8, 1/5}],
v \[Distributed] UniformDistribution[{1*^-8, 1/5}]}];

Block[{Integrate = NIntegrate}, PDF[pmd, 3.]] // AbsoluteTiming
{0.254763, 0.0171523}


Compare this with

PDF[pmd, 3.] // AbsoluteTiming
{114.855, 0.0171523}


Plot[Block[{Integrate = NIntegrate}, PDF[pmd, x]], {x, 0, 5}] You need to define the values of m and v.

Manipulate[
Plot[PDF[pmd /. {m -> m0, v -> v0}, x], {x, 0, 0.2}], {{v0, 2}, 1,
5}, {{m0, 1}, 1, 4}] 