Plotting average of many empirical cumulative distribution functions

I have a code in which I start a figure, make hold on and repeat a for cycle where at the end of each repetition I plot an empirical cumulative distribution function. So at the end I have in the same figure many ecdf (they are defined on the interval [0,1] and take value, obviously in [0,1]. How can I add to the same figure the average of these functions? I mean, is there a command that memomrizes the values taken by each function and thanks to which I can plot the average of these functions?

Answer 1

[Jeff Miller]

I'm pretty sure there is no function to do that. To compute the average function by Vincentizing, you first choose a set of CDF values where you will compute the averages & initialize a vector to hold the totals at each CDF value, say

CDFvals = 0.01:0.01:0.99;
ttlCDFs = zeros(size(avgCDFs));

Then, each time you go through the loop and make a new eCDF, you find the score at each avgCDF value (e.g., with one of the methods described in iecdf from FileExchange), something like

[f,x] = ecdf(y);  % y is your data for the empirical CDF computed in this pass through the loop.
for iCDF = 1:numel(avgCDFs)  % Probably can be vectorized for speed, but this shows the idea
    pos = find(CDFvals(iCDF)<=f,1);
    xq = x(pos);
    ttlCDFs(iCDF) = ttlCDFs(iCDF) + xq;
end

Then at the end you can compute & plot the average data value at each CDFval,

avgCDFs = ttlCDFs / NumberOfCDFsBeingAveraged;  % Same as the number of passes through the loop
plot(CDFvals,avgCDFs)

[kevin cecere palazzo]

How should I define avgCDFs? I don't clearly get what it is and what is its dimension, it is liked to ttlCDFs but which one is defined first?

[Jeff Miller]

You don't need to define it separately from its computation, but if you want you can include

avgCDFs = zeros(size(CDFvals));

[kevin cecere palazzo]

Last question, I did not get what exactly do these two lines:

pos = find(CDFvals(iCDF)<=f,1);
    xq = x(pos);

should'nt I write "last" after 1 in the first of the two lines?

[Jeff Miller]

Those lines, which I may have miscopied from eicdf, are supposed to find the x value with the indicated CDFval. I think you are right about 'last'. Or maybe it should be

pos = find(f<=CDFvals(iCDF),1);

Just look at an example or two and it will be easy to tell.