I would like to evaluate the PDF of a custom ProbabilityDistribution at the min and max values. However, PDF[...] returns 0 at the boundary conditions. Is there an elegant way to prevent this? Example:
dst = ProbabilityDistribution[2 x, {x, 0, 1}];
PDF[dst, 0.99999] (* = 1.99998 *)
PDF[dst, 1] (* = 0 *) (* I would like this to return 2 *)
The docs say that
the pdf is taken to be zero for $x < x_{min}$ and $x > x_{max}$
It seems inconsistent that the PDF is forced to zero at $x = x_{max}$.
PDF[ProbabilityDistribution[f, {x, 0, 1}], x]– rm -rf♦ Aug 1 '12 at 7:58Plot[PDF[dst, x], {x, -1, 2}, ExclusionsStyle -> Directive[Gray, Dashed]]does exactly what you would expect. Same forIntegrate[PDF[dst, x], {x, -\[Infinity], \[Infinity]}]– Sjoerd C. de Vries Aug 1 '12 at 9:04Limit[PDF[dst, x], x -> 1 , Direction -> 1]andLimit[PDF[dst, x], x -> 0 , Direction -> -1]to get2or0respectively. – Artes Aug 1 '12 at 9:35