# How to pick the j-th percentile of a vector?

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MRC on 2 May 2014
Commented: Siddhartha on 7 Apr 2016
Hi, I have a matrix A nx1, e.g.
A=randn(200,1);
II want to pick the element of A which is the 25th percentile above the minimum in A. How can I do it?
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Siddhartha on 7 Apr 2016
function val = SpecialPercentile(arr, pct)
len = length(arr);
ind = floor(pct/100*len);
newarr = sort(arr);
val = newarr(ind);
end
Then call this function p = SpecialPercentile(A, 25);

Star Strider on 2 May 2014
If you don’t have the Statistics Toolbox, this doesn’t replicate the prctile results exactly, but it’s close:
pctl = @(v,p) interp1(linspace(0.5/length(v), 1-0.5/length(v), length(v))', sort(v), p*0.01, 'spline');
where v is the data vector and p is the percentile. You would call it as:
p = pctl(A, 25);

Justin on 2 May 2014
Edited: Justin on 2 May 2014
Is the function prctile what you are looking for?
It is in the statistics toolbox. You can use it to find the specific percentile you are looking for (in this case 25) and then find the minimum element in A greater than the percentile number.
Let me know if this makes sense or if you would like an example.

Image Analyst on 2 May 2014
Do you mean like this:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 30;
A=randn(200,1);
sortedA = sort(A)
minA = min(A) % Just for information - not used
% Get cumulative distribution function
cdf = cumsum(sortedA - sortedA(1))
bar(cdf);
% Normalize
normalizedCdf = cdf / cdf(end)
% Plot it.
plot(sortedA,normalizedCdf, 'LineWidth', 2); % Show in plot.
grid on;
title('Cumulative Distribution Function', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Find index where it exceeds 25% for the first time
indexOf25Percentile = find(normalizedCdf > 0.25, 1, 'first')
% Find value where it exceeds 25% for the first time
valueOf25Percentile = sortedA(indexOf25Percentile)
% Plot vertical bar there
line([valueOf25Percentile, valueOf25Percentile], [0, .25],...
'Color', 'r', 'LineWidth', 2);
% Plot horizontal bar there
xl = xlim;
line([xl(1), valueOf25Percentile], [0.25, .25],...
'Color', 'r', 'LineWidth', 2);
message = sprintf('25 Percentile happens at %f (index %d)',...
valueOf25Percentile, indexOf25Percentile);
uiwait(msgbox(message));
Image Analyst on 2 May 2014
You can do it that way if you want. It's like I'm taking the rank of the y values and you're taking the rand of the x values. Notice on the red lines that my 25% is 25% of the y (which happens at an x of -0.17), and yours would be the 25% of the x (-2.25) and you'd read off the y that you get at x = -2.25 (which is like 0.01 or something). If the cdf is linear, like you'd get with a uniform distribution, then they'll give the same value. If not, then they'll be different.