Why does lognpdf not integrate to 1?

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Jessica
Jessica on 25 Oct 2014
Commented: Jessica on 25 Oct 2014
Hello all,
We know by definition that a pdf must integrate to 1, but I'm finding in my code that this is not the case for a pdf I create using lognpdf and I am wondering why. Can you please help me?
increment = 0.01 ;
x = 0:increment:1 ;
mean_val = 0.25 ;
sigma_val = 0.69 ;
y = lognpdf(x,mean_val,sigma_val) ;
>> trapz(x,y)
ans =
0.358554747437567
You can see that the integral (approximated by the trapezoidal method) is significantly below 1. Why?

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Accepted Answer

the cyclist
the cyclist on 25 Oct 2014
Doesn't it integrate to 1 over the interval [0,infinity], not [0,1]?
  1 Comment
Jessica
Jessica on 25 Oct 2014
Ugh. You're right. I had been working with Beta distributions the whole time before this, so my frame of reference was skewed. That's silly.
Now, how to get the lognormal pdf to behave the way I want it to between 0 and 1...anyway, thank you.

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