Hi all,

Many thanks for your prompt answer! The example I gave is in fact in the Maple examples, I have no specific interest on this distribution but in the algebra/transformation of independent random variables. If Maple fails on this elementary example, it makes me suspiscious for all the other transformations, which is the main trouble.

An elementary computation gives the following expression for the PDF:

p(x)=piecewise(x<=-1,0,x<1,Sum(exp(-(arccos(x)+k*Pi)^2/2),k=-infinity..infinity)/sqrt(2*Pi*(1-x^2)),0)

Maple mises the fact that the cosine function is a C^1-diffeomorphism on each of the open intervals (k*Pi,k*Pi+Pi) for k in Z, and the change of variable has to be made on each of these intervals, then the different contributions have to be added.

The fact that the PDF is discontinuous on both -1 and 1 is not surprising as the cosine function has these values as extrema. It is a common property of the distribution of random variables transformed by functions who have extrema in the range of the random variable. It is no worse than a Beta distribution with shape parameters less than 1. I chose to illustrate the problem using the CDF as it is clear that the correct value should be 1. Even if the value given by Maple is close to one, it is misleading as it is given in closed form, so it should be exactly 1. If you replace Normal(0,1) by Normal(0,10) you get erf(Pi*sqrt(2)/20) as a limit, which is approximately equal to 0.2465999, clearly wrong andno more close to 1!

It is my first bug report, and I didn't found a way to report bugs on the maplesoft website. Could you please give me a pointer to the correct page?

Best regards,

Régis