MATLAB Answers

area under a pdf not 1?

10 views (last 30 days)
Abhinav
Abhinav on 20 Jul 2017
Commented: Abhinav on 20 Jul 2017
I have convoluted two pdfs. Both of my pdfs are exponential with lambda=10 and 20, respectively. I have used the following code:
fun1=@(x)exppdf(x,10);
fun2=@(x)exppdf(x,20);
x=0:30;
y=conv(fun(x),fun2(x));
The code above gives the vector y with 61 elements in it. When I used the 'trapz(0:60,y)' function to find the area under the curve y, it gives 0.80 as output. However, the area should be one since y represents a pdf. I suspect that it is due to the error associated with integration via 'trapz'.
But I need to confirm that I am getting a valid pdf. What function can I use instead of trapz. I cannot use the function 'integral', because it requires functional form of convolution output which I don't have.
Any suggestions?

Accepted Answer

Star Strider
Star Strider on 20 Jul 2017
It has approximately unity area:
fun1 = @(x)exppdf(x,10);
fun2 = @(x)exppdf(x,20);
y = @(x) conv(fun1(x),fun2(x));
x = linspace(0, 100);
yint = trapz(y(x))
yint =
1.0474
It is necessary to bear in mind the support of PDFs. Integrate it over its entire length.
  5 Comments
Abhinav
Abhinav on 20 Jul 2017
Okay.

Sign in to comment.

More Answers (0)

Community Treasure Hunt

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

Start Hunting!