Info

此问题已关闭。 请重新打开它进行编辑或回答。

How to integrate a distribution function for a specific interval?

1 次查看（过去 30 天）
Nina
Nina 2017-11-6
关闭： Nina 2018-4-17
I computed two distribution function:
[distribution_1,x]=ecdf(X); Distribution_2= f(distribution_1);
Now I want to integrate Distribution_2 over the interval [a,b] and tried to use q = integral(fun,xmin,xmax) but I have trouble creating the function handle "fun" in my specific case (since I cannot create the connection to x?)
Thankful for any advice!
  5 个评论
显示 3更早的评论
Nina
Nina 2017-11-6
Concerning the distortion function f: Distribution_2=1-(1-distribution_1.^(1/(1+g))).^(1+h) eg. with g=0.1 and h=0.2

此问题已关闭。

采纳的回答

Robert
Robert 2017-11-6
To make your empirical CDF into a function that integral can use, you should interpolate distribution_2. Because of the way the CDF is defined, I recommend you interpolate based on the previous value. The first value of x is a duplicate of the second, but for use with interp1(..., 'previous') it should be a (finite) number less than any you plan to use. -realmax should do the trick.
x(1) = -realmax;
f_dist2 = @(new_x) interp1(x, distribution_2, new_x, 'previous', 'extrap');
integral(f_dist2, -1, 1)
  3 个评论
显示 1更早的评论
Nina
Nina 2017-11-7
Another problem came up for the code when using integral(f_dist2,0,inf). Do I need to take into account anything extraordinary in this infinity case? Would be very pleased to receive another answer :)
Below the warning I get when running the code: Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.7e-04. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.

更多回答（1 个）

David Goodmanson
David Goodmanson 2017-11-6
编辑：David Goodmanson 2017-11-6
Hi Nina,
If this is not a misinterpretation of the problem, then it seems to work. I am assuming that the function ecdf is already on the Matlab path.
g = .1; h = .2;
fun = @(x) 1-(1-ecdf(x).^(1/(1+g))).^(1+h)
integral(@(x) fun(x), 2,3)
function a = ecdf(x) % for demo purposes
a = sin(x);
end
I'm curious about the idea of integrating a cdf, could you perhaps comment on that?
  1 个评论
Nina
Nina 2017-11-7
Hi David, thanks for your answer, your code would work if X=x, but this is not the case here: Interpolation can solve this problem as described by Robert below :)

此问题已关闭。

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by