If you have the custom PDF function (call it custPDF), then you can compute the custom CDF function something like this:
function p = custCDF(x)
p = integral(@custPDF,LowerBound,x); % Modify AbsTol and RelTol to suit your needs
end
where LowerBound is some minimal value for your custom distribution.
Then you should be able to get the inverse CDF with this:
function x = custiCDF(p)
x = fzero( @(x) custCDF(x)-p, [LowerBound,UpperBound] );
end
where UpperBound is a maximal value.
It might be pretty slow, but it should work.
