I got this answer earlier today for how to distort a random number seed toward one bound of the range:
var random = Math.pow(Math.random(), 2);
But that obviously distorts it along an exponential curve.. How can I make it linear?
Also, kind of relevant: I just created this simple script to visualize different types of distributions. It may be helpful for this question: http://jsfiddle.net/RTbrL/
It sounds like you are describing a one-sided triangular distribution.
If so, try
var random = 1.0 - Math.sqrt(Math.random());
or
var random = Math.abs(Math.random() - Math.random());