Why Is My TI-89 Giving Infinity for Log-Normal PDF Integration?

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SUMMARY

The discussion centers on the integration of the probability density function (PDF) for the log-normal distribution using a TI-89 calculator. The user reports that their integration from 0 to infinity yields an incorrect result of infinity instead of 1. The correct formula for the PDF, as clarified by another user, is e^(-((ln(x) - 1)^2)/2)/(sqrt(2*pi)*x), which resolves the issue by properly adjusting the exponent in the equation.

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  • Understanding of log-normal distribution and its properties
  • Familiarity with probability density functions (PDFs)
  • Basic knowledge of integration techniques
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  • Review the log-normal distribution and its applications in statistics
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Statisticians, students studying probability and statistics, and anyone using TI-89 calculators for mathematical integration of probability density functions.

oneamp
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I am using the PDF for log-normal distribution, which I'm referencing off the wikipedia page:
here. I am integrating from 0 to infinity with my TI-89. It is not giving me 1, as I'd expect from a PDF, but is giving me infinity. Here is how I'm entering it in the calculator (I've tried a few variations):

e^(-((ln(x-1))^2/2))/(sqrt(2*pi)*x)

mu and sigma are one, so it simplifies to this. What is going on :(

Also I just tried integrating from 0 to 12, and it also says infinity. I guess I am doing something wrong :(


Thank you
 
Last edited:
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Your exponent is wrong. It should be ((lnx - 1)2)/2.
 
thank you
 

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