Randomly dividing an integer (non-uniform distribution)

I am trying to write a code that randomly divides a number N into M parts (in other words, I want to generate M random numbers whose sum adds up to N). However, I want to allow the generated numbers to vary considerably in magnitude.

My current code generates numbers that are all in the same ballpark:

For instance, for

, it yields:

    0.0414    0.0326    0.0786    0.0778    0.0608    0.0290

As one can see, the number

is so evenly distributed that all generated numbers have the same (or close) orders of magnitude.

Is there a simple way to tweak this code so that it can generate numbers that are widely different in magnitude (e.g. 0.7 and 0.01)?

Any suggestions would be greatly appreciated.

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There are any number of ways to do that, depending on exactly what you mean by “considerably”. Here are a few:

%%  Generate progressively smaller numbers by generating each new one as a uniform(0,1) fraction of
% what is left of your total.
M=20;
n = rand(1,M);

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