Calculate percentiles from empirical PDF values

How can I calculate percentiles such 10%, 50% (median) and 90% based on the empirical probability density values?

[Torsten]

What do you mean by "empirical probability density values" ? You mean discrete values (x,y) of the probability density function ?

[Sajid Afaque]

yeah i have a similar issue how can we calculate from discrete value (x,f) of eCDF ?

Answer 1

[David Rogers]

The best way is to use the cumulative distribution function (CDF) as a lookup table. The CDF is the integral of the PDF. Starting from raw data, you could use ecdf:

[f, x] = ecdf(random('wbl', 3,1,15,1));

You could also get a CDF starting from a vector of normalized histogram counts by creating a cumulative sum,

f = cumsum(prob .* (x(2:end)-x(1:end-1)))

Where x is a vector of start and stop positions for each bin and "prob" is the empirical probability distribution in each bin.

To find the 10th percentile, you want the x coordinate between f < 0.1 and f > 0.1:

n = find(f>0.10, 1)
[x(n-1), x(n)]