Hi all,
I have been going through a proof, but can't seem to make sense of a step, I am sure its trivial, but I can't seem to see it!....
Let be a uniform variable on and let , find the density function of .
Find CDF first:
Now its the last step I cant seem to see; where does the 1 come from? I can see teh rest of the proof from that point on, but have problems seeing what happened in this step...
Many thanks for reading!
As an aside, the uniform distribution is much under-used.
When it comes to fitting data the least-squares method is almost always used without thinking.
But, in many circumstances the L-1 norm is far more accurate( admittedly, when it is out, then it is far out), but it is very neglected.
It is used all the time in fact. All pseudo random number generators attempt to produce uniformly distributed numbers on [0,1), and they are then transformed to other distributions as required. This would possibly make the uniform distribution the most frequent use of any probability model.
But computationally intensive, so until possibly the last 20-30 years impractical.When it comes to fitting data the least-squares method is almost always used without thinking.
But, in many circumstances the L-1 norm is far more accurate( admittedly, when it is out, then it is far out), but it is very neglected.
CB