Find percentile corresponding to an input value

I'm trying to find a MATLAB function that is similar to the PERCENTRANK formula in Excel. With this formula you enter an array and a scalar and it tells you what percentile that scalar corresponds to.

Answer 1

[Walter Roberson]

PERCENTRANK = @(YourArray, TheProbes) reshape( mean( bsxfun(@le, YourArray(:), TheProbes(:).') ) * 100, size(TheProbes) )

This accepts a vector or array of data, and an array of probe positions (could be a scalar), and returns an array of percentiles the same size as the probe positions, considered over the entire content of the data array (not per row or per column)

[Alex]

I'm new to Matlab and I'm interested in this solution, how can I use it? Could you explain what are probe positions please?

Thanks

[Wenersamy de Alcantara]

Hi, Alex, the algorithm of the suggested PERCENTRANK function basically averages the result of a logical comparison.

For example, in the vector (6 numbers drawn from a discrete uniform distribution):

[23 45 98 2 81 17]

If you compare it with, say, 30: [23 45 98 2 81 17] <= 30, you'll have:

[1 0 0 1 0 1]

If you avarage the results of the comparison, you'll have:

3/6 = 0.5 or 50% percentile.

Of course, the approximation gets better with a bigger sample.

In other words, you can implement excel function PERCENTRANK.INC(matrix,k) by just using: mean(matrix<=k).

Note that they are not exactly the same algorithm, but they get closer as the size of "matrix" increases.

[Miguel Lovino]

Hi Walter,

this code works perfectly for a vector (lat - lon -time varying). I want to adapt it to an array array of 121 * 121 * 2995 (it's lat-lon -time). That is, for a given lat-lon, it works. I try to rewrite as:

A = ncread('ERA5_pentads_sm_l123_1979-2019.nc','sm');

B = ncread('ERA5_pentads_sm_l123_1979-2019.nc','sm');

[n,m,t]=size(A);

As = zeros(n,m,t);

for ii=1:n

for jj=1:m

PER = @(A,B) reshape( mean( bsxfun(@le, A(ii,jj,:), ipermute(A(ii,jj,:),[3 2 1])))...

* 100, t, []);

As (ii,jj,:)= PER (A);

end

end

It works, but it seems that lat-lon points are not correct.

I really appreciate some help,

Best

Miguel

Answer 2

[Stefano Crema]

Great, compact and handy solution, thanks Walter!