I've been applying the probability integral transform as shown here to standardise date for input into a neural network:
I want to standardise the data that is wiebull distibuted by mapping it to standard normal:
The original histogram is shown below:
When I transform to the standard Normal I get the histogram shown below, which doesn't look very Normal. I don't want the big gap I want the transformed histogram to look as much like a standard normal as possible. Is there anything else I can do?
Here is the pdf of the inverse CDF it is approximately flat, When I normalize by the data set size the resultant sum is approximately 0.5? I would expect it to be approximately one? Should I be normalising the data by some other value other than the size of the data set?