MATLAB: How to pick the j-th percentile of a distribution

percentileStatistics and Machine Learning Toolbox

Hi all,

I have some data and I want to pick the j-th percentile of the distribution.

Here an example:

a=2000;
b=300;
c=a+(b)*randn(100,1);
cdfval = fitdist(arg_1, 'normal');

So how can I get the 50° percentile of the distribution, that it is 2000?

thanks

Best Answer

Since you have the Statistics Toolbox, use the prctile function.

Related Solutions

MATLAB: How to pick the j-th percentile of a vector

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);

in your example.

MATLAB: Fitting lognaormal distribution with constraints

The lognormal distribution has two parameters (mu & sigma). If you impose two constraints (namely that the fitted distribution has to have the same 95th and 99th percentile values), then you've determined your parameters. So you're not really fitting the data and constraining the percentiles -- you're fitting the data by constraining the percentiles.

That doesn't sound like a particularly safe thing to do, when the constraints are -- by definition -- outliers, but I'm no statistical guru, so...

Assuming that's really what you want to do:

% Create some data
w = random('lognormal',4.5,0.25,[100 1]);
% Get the empirical quantiles
q1 = quantile(w,0.95);
q2 = quantile(w,0.99);
% Define function to minimize
f = @(p) norm([logninv(0.99,p(1),p(2))-q2;logninv(0.95,p(1),p(2))-q1]);
% Get parameters for MLE fit
pmle = lognfit(w)
% Use them as a starting point for constrained fit
pcon = fminsearch(f,pmle)
% View results
ww = linspace(0,200,501);
ymle = logncdf(ww,pmle(1),pmle(2));
ycon = logncdf(ww,pcon(1),pcon(2));
plot(ww,ymle,ww,ycon,q1,0.95,'o',q2,0.99,'o')

You should see that the two percentile points in the resulting graph lie on the green curve, but probably not on the blue curve. The blue is the unconstrained fit, from lognfit; the green is from forcing the cdf to go through the empirical quantiles.

pmle is a vector of mu and sigma from a regular MLE fit; pcon is a vector of the parameters from the constrained fit.

Best Answer

Related Solutions

MATLAB: How to pick the j-th percentile of a vector

MATLAB: Fitting lognaormal distribution with constraints

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