HELP! Reading a probability from a CDF plot

I have created a CDF plot of some temperature data, and I need to find exceedence probability. Is there a way to input a specific number (i.e. an x-value) and have MATLAB return the exceedence probability?

Answer 1

[Oleg Komarov]

Give a look at this FEX submission: exceedance probability.

Oleg

Answer 2

[Matt Tearle]

You basically want an inverse CDF calculation (based on measured data, rather than a formula)?

% Make some fake data
x = -4:0.2:4;
y = (1+tanh(x))/2;

% Pick a probability
yval = 0.72;
% Interpolate to find x such that y(x) = yval
f = @(t) interp1(x,y,t,'pchip') - yval;
xval = x(find(y>=yval,1,'first'))
xval = fzero(f,xval)
% See the result
plot(x,y,'o-',xval,yval,'*')

The idea is to find the first data point that exceeds the given probability, then use that as an initial guess to a root-finding algorithm to find the actual x such that y(x) = prob. The tricky thing is that you have to interpolate to get a function to do root-finding on. Hence the use of interp1.

Answer 3

[Adele]

Thanks for the advice, everyone!

I was able to ask my instructor and he told me to use the command "ecdf(input_data)" which gave me 2 matrices, one containing the temperature values I was given and the other contained the cdf values corresponding to the individual temperature values. From here, I was able to interpolate and find the exceedence probability.

I didn't try the other approaches because I am a beginner and didn't really understand what was going on.

[Matt Tearle]

My code was intended to show how to do the interpolation (your question implied you already had the empirical CDF).