title: Is there a correct way of taking a histogram of ratios?
body: <p>My problem is as follows;  I have two vectors <code>u</code> and <code>v</code>.  I have computed a table of cross-ratios like so:</p>
  
  <pre><code>[ u1/v1, u1/v2, u1/v3, u1/v4, ... ]
  [ u2/v1, u2/v2, u1/v3, u2/v4, ... ]
  [ u3/v1, u3/v2, u1/v3, u3/v4, ... ]
  [ u4/v1, u4/v2, u1/v3, u4/v4, ... ]
  [ ...
  </code></pre>
  
  <p>My task now is to compute a histogram of these cross ratios.  However, it is clear that using linear histogram bins would not make sense - any ratios below 1 would have a far lower sample resolution than the ratios above 1, and the long-tailed nature of the ratio distribution means that my choice of bins would be skewed heavily by large values.</p>
  
  <p>So, my question is: is there a 'correct', or at least better, choice of histogram bins (or equivalently, a transformation to apply to the data) for this situation?  I can see that the  <a href="http://en.wikipedia.org/wiki/Cauchy_distribution" rel="nofollow" title="Cauchy distribution">Cauchy distribution</a> might be relevant although I'm quite sure how.</p>
  
  <p>Many thanks in advance.</p>