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# Returns weighted percentiles of a sample

### Durga Lal Shrestha (view profile)

16 Oct 2007 (Updated )

Returns weighted percentiles of a sample with six algorithms given weight vector

File Information
Description

The idea is to give more emphasis in some examples of data as compared to
others by giving more weight. For example, we could give lower weights to
the outliers. The motivation to write this function is to compute percentiles
for Monte Carlo simulations where some simulations are very bad (in terms of
goodness of fit between simulated and actual value) than the others and to
give the lower weights based on some goodness of fit criteria.

USAGE:
y = WPRCTILE(X,p) % This is same as PRCTILE
y = WPRCTILE(X,p,w)
y = WPRCTILE(X,p,w,type)

INPUT:
X - vector or matrix of the sample data
p - scalar or a vector of percent values between 0 and 100

w - positive weight vector for the sample data. Length of w must be equal to either number of rows or columns of X. If the weights are equal, then WPRCTILE is same as PRCTILE.

type - an integer between 4 and 9 selecting one of the 6 quantile algorithms.

OUTPUT:
y - percentiles of the values in X
When X is a vector, y is the same size as p, and y(i) contains the
P(i)-th percentile.
When X is a matrix, WPRCTILE calculates percentiles along dimension DIM which is based on: if size(X,1) == length(w), DIM = 1; elseif size(X,2) == length(w), DIM = 2;

EXAMPLES:
x = randn(1000,1);
w = rand(1000,1);
y = wprctile(x,[2.5 25 50 75],w,7)

Acknowledgements

This file inspired Quantile Calculation.

MATLAB release MATLAB 7.5 (R2007b)
12 Feb 2013 Felipe G. Nievinski

### Felipe G. Nievinski (view profile)

For those looking for a weighted median: wmedian = @(X) wprctile(X,50);

03 Jun 2010 Lorenz

### Lorenz (view profile)

I claim that this can be implemented in expected linear time. As you are using sorting, you have at least O(n log(n)), assuming Matlab uses comparison-based sorting (which is proven to need at least n log(n) - O(n) element comparisons in average).

Comment only
02 Apr 2008 Durga Shrestha

Thanks for pointing it. Indeed I have used the the formula pk = k/n (type = 4 in R package). What you suggested is type 5 (p(k) = (k - 0.5)/n)which is used in MATLAB.

I have updated the code using 6 different algorithm to compute the quantile.

Comment only
31 Mar 2008 Li Li

It's all right except that the coordinates fed into the interp1q function is incorrect. However, it's a 2-line fix:

After the line "cumW = cumsum(sortedX(:,2));", it should read
coord = (cumW - sortedX(:,2)/2)./(sum(sortedX(:,2)));
q = [0;coord;1];

27 Feb 2008 Durga Shrestha

To A P

Please mention what is incorrect. Do you mean underestimate the median? But if you see the figure WPRCTILE overestimates the median than by PRCTILE. However this depends on the weight vector.

Comment only
05 Feb 2008 A P

INCORRECT! This understates the median.