<p>A way to get what you want is to generate truncated normally distributed random radii r with \sigma=1 in a range +-R and uniformly distributed random values \theta in 0..pi for the polar angle.  If A and B are the major and minor axes aligned with x and y, then the points with respect to the origin are</p>

<pre><code>x = r A/R cos \theta,   y = r B/R sin \theta
</code></pre>

<p>When you choose parameter R to be large, the values will be concentrated toward the center of the ellipse. When it's small, they'll be evenly distributed across it.</p>

<p>Generating pseudo random values that are truncated-normally distributed is not trivial, but not too hard either.  See e.g. <a href="http://arxiv.org/pdf/1201.6140.pdf" rel="nofollow">Chopin's paper</a> for a good discussion. <a href="http://miv.u-strasbg.fr/mazet/rtnorm/" rel="nofollow">This C++ implementation</a> looks useful.</p>

<p>If you don't care about all the points lying inside the ellipse, you can use the full normal distribution. The Box Muller algorithm for this is very simple to implement, and it's built into many libraries <a href="http://docs.oracle.com/javase/7/docs/api/java/util/Random.html#nextGaussian()" rel="nofollow">including Java's</a>.</p>
Random point within oval with higher probability for a point closer to the centre?
<p>I feel like the question is quite descriptive but to illustrate it in words.</p>

<p>Picture a radial gradient (black in centre, white on edge) I want to generate a random point that is more likely to fall in the black, less likely to fall in the grey, and even less likely to fall in the white.</p>

<p>Could someone point me in the right direction? I'm quite stumped :/</p>