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Why does lognpdf not integrate to 1?

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Jessica
Jessica 2014-10-25
评论： Jessica 2014-10-25
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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the cyclist
the cyclist 2014-10-25
Doesn't it integrate to 1 over the interval [0,infinity], not [0,1]?
  1 个评论
Jessica
Jessica 2014-10-25
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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