MATLAB: Does lognpdf not integrate to 1

lognpdfMATLABpdfprobability density functiontrapz

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?

Best Answer

Doesn't it integrate to 1 over the interval [0,infinity], not [0,1]?
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