Generate random numbers with custom PDF

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Michael on 11 Jun 2012
Edited: Walter Roberson on 10 Jun 2018
Hi, as it may become clear I'm fairly weak on probability distributions
I want to generate a set of random numbers between 0 and 1, but able to alter the weighting of these numbers. For example if I could input some sort of "bias" parameter which determines the extent to which the numbers tend to be closer to 0 than to 1, for example.
I don't know which of MATLAB's many distributions I should use. So far I've been using the uniform distribution and taking it to the power N, but N=0.5 seems to give an entirely different PDF shape (in favour of numbers close to 1) than the intended opposite bias, N=2 (in favour of numbers close to 0). Squaring it seems to favour small numbers far more than sqrt-ing seems to favour large numbers, so I've rejected this approach as unfair.
Is there a common distribution for this? Numbers have to be between 0 and 1 and I want to take control of how close they are, on average, to either.
Thanks Mike

Image Analyst on 10 May 2013
In general, you basically compute the CDF of your PDF function and invert it. Go here for a generally applicable explanation of how to do it: http://en.wikipedia.org/wiki/Inverse_transform_sampling
Martins Ezuma on 10 Jun 2018
Thanks

Pantelis Sopasakis on 10 May 2013
You may consider using this PDFSampler. I believe, it does exactly what you need. You just need to specify how you want your samples to be distributed, e.g. you may provide their histogram.

Tom Lane on 11 Jun 2012
If you have the Statistics Toolbox, then take a look at the beta distribution. Use it with disttool to see how the parameters affect the distribution, randtool to see what a random sample from this distribution looks like, and betarnd to generate your own sample from the command line or inside a function.

Ka Mirul on 14 Nov 2017
Edited: Walter Roberson on 10 Jun 2018
I have create a video about generating random number in MATLAB https://www.youtube.com/watch?v=MyH3-ONYL_k