Using MATLAB, what is the best way to find the integral of a bounded range of a CDF?

Using MATLAB, what is the best way to find the integral of a bounded range of a CDF. I've heard of trapz, cumtrapz, etc. but I do not know the best way to proceed for integrating CDFs. Please refer to the following code:

u = 1;
s = 1;
X = random('Normal',u,s,1,10000);
pd = makedist('Normal','mu',u,'sigma',s);
xAxis = min(X):.0001:max(X);
c_pd = cdf(pd,xAxis);
r = icdf(pd,[.3,.6]);
plot(xAxis,c_pd)

Basically, I am trying to integrate c_pd between the corresponding X values for .3 and .6 (found by using icdf). However, c_pd is a vector and not the actual cdf function. Does anyone have ideas on the best way to find the integral of this regardless of the distribution type (i.e. Normal, Rician, etc.)? Please advise. Thank you.

Answer 1

[Mike Hosea]

Well, you have the function as well, not just the vector. If I understand you correctly,

integral(@(x)cdf(pd,x),r(1),r(2))

[Aaron]

Really?! The cdf(pd,x) used in your code would not return a vector but would actually return a function to be integrated??

[bym]

Mike is using an anonymous function ( notice the @(x) preceding the cdf(pd,x))

[Aaron]

Pardon my ignorance, but does that mean that the anonymous function happens to be the Normal CDF function hidden within the MATLAB source code?

[Tom Lane]

It is an invocation of the cdf method on your pd object. So pd is built into the function definition, and x is an input argument. Presumably running that function does involve running the normcdf function or something similar.

[Mike Hosea]

Aaron, are you all set now? Anonymous functions serve two purposes. One is to fix variables in a function definition, and the other is to provide a quick way of defining functions (versus writing a .m file). Here CDF is formally a function of two variables, pd and x, and we want a function of one variable, x. In general, if we have a function of two variables f(x,y), the anonymous function g = @(x)f(x,y) defines a function g(x) based on value of y at the moment that we created g. So g = @(x)cdf(pd,x) creates a function g(x) that is based on the value of pd at the moment we created g. Note that changing pd doesn't change g. You have to re-define g via g = @(x)cdf(pd,x) to pick up the new value of pd. -- Mike

[Aaron]

Yes, thank you very much. And, I appreciate the clarification on needed to re-define g if pd changes. I would not have known!

[Aaron]

And thank you to everyone for the help!