Now, I’ve decided to break down the Barton and Schruben (1993) method into two parts as you need to know what an empirical cumulative distribution function (eCDF) is first.  That’s empirical, don’t you know!  So what is it?  Well, it’s basically computes all the number of events that can happen at a certain point over the total number of points.  So lets say Randy has an equal chance of catching Anton in one of the six justified realms, i.e., a 1/6th chance.  If he looks into one realm, his chances of finding Anton is 1/6th.  But if he thoroughly searches that realm and starts looking into a second realm, his chances jump up to 2/6.  And then when he moves up to a third realm, his chances go up to 3/6, or 1/2.  Yeah, I know I’m getting lazy with this post.  I mean … how could Randy exhaust every nook and cranny of every dimension and how could I assume that each dimension carries an equally probability?  Well, I don’t and that’s the thing.  That’s why we will continue talking about mapping the eCDF onto other scales.  Next time — until then:

Yeah, another play on Barton and Schruben (1993).  Admit I’m kinda getting lazy with the pictures too — will work on that, promise!