How to generate perfectly distributed numbers for an arbitrary probability distribution function ?

My goal is to create a incremental vector like:

x = linspace(min,max,N);

But the points are distrubuted according to an arbitrary probability distribution function, instead of being evenly spaced.

The only way I can think of is:

x = random('pdf',...,[N 1]);
x = sort(x);

However this is a twisted and nastly method, and only works with a very large N.

The result is still ugly even with N = 1000

x = random('gamma',2,2,[1000 1]);

If I have a perfecly distributed data, instead of random numbers, I only need to sort it to get my incremental vector.

Unfortunaly I only know how to do the opposite: data -> bin -> pdf, which does not work the other way around: pdf -> bin x-> data

Thanks in advance !

[Walter Roberson]

I am not clear as to what you are doing, but perhaps https://www.mathworks.com/help/stats/prob.normaldistribution.icdf.html

[Jeff Miller]

Like Walter, I think icdf will give the nice even data values that you want. The only trick is to generate the p values for icdf with linspace between 0 and 1, something like

pd = makedist(???);  % create the arbitrary distribution that you want to use
p = linspace(0.001,0.999,N);  % evenly spaced cumulative p values for your data points
x = icdf(pd,p);  % the x values corresponding to those p values