I have a distribution that is skewed to the left (i.e. a lot of low values, aka positive skew - verified)
Basically, I have either a lot of similar low [~minimum] values, or 0 values, or something like 1 value that is the only value below the median value.
The data has already been normalized to 0 to 100% based on an ECDF run [transformation]. AKA an Empirical Cumulative Distribution Function, very similar to a rank transformation, it's very simple. Is value equal to or less than the rest of the values, if not, then count the number of values less than or equal to current value, and count that towards that values overall Cumulative Distribution Function.
So... is there a simple way to mean adjust the ecdf distribution to a .5 mean, and slope the data from 0 to 100%
My first guess was to track the difference from a .5 mean.
My second guess was to derive the # of unique #'s in my [skewed] distribution to establish categories I needed to divide by from my difference from mean.
Sample set of data: 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
After ecdf conversion 0.05 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 1 1 1 1 1 1 1 1 1
I had one idea to factor DOWN anything equal to or below median by .5
our desire to achieve .5 mean is because we are combining the distribution with other distributions that after ecdf conversion already have a ~.5 mean. The problem with our skewed data set is it's promoting low skewed values to high %'s and we don't want to do that. So, we would prefer to achieve a .5 with the skewed data.