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I am unable to compute a complex integral which uses the pdf of log-normal distribution. Hence, I want to replace the pdf of log-normal distribution with an alternate function(s) (piece-wise approximation is also fine) $f_X$$(x)$ which is a function of $\mu$ and $\sigma^2$ so that it best approximates the pdf of log-normal distribution.

How can I approximate the pdf of log-normal distribution? Which function can I use?

P.S: $\mu$ and $\sigma^2$ are the mean and variance of the gaussian random variable using which the log-normal variable is derived.

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You can try to approximate the pdf on a closed interval $[\mu - \alpha \sigma,\mu + \alpha \sigma]$ by an interpolation polynomial.

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  • $\begingroup$ Can you please elaborate your answer by considering an example? $\endgroup$
    – skt9
    Jun 1, 2016 at 10:10
  • $\begingroup$ @skt9 en.wikipedia.org/wiki/Lagrange_polynomial#Example_1 $\endgroup$
    – Dark
    Jun 1, 2016 at 14:04
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    $\begingroup$ Thanks, but I don't want to use numerical methods(interpolation etc), I would like to know if it is possible to replace the pdf by an alternative function under some conditions, like say a normal distribution when $\sigma$<<$\mu$(just an example, need not be true) or something like that? $\endgroup$
    – skt9
    Jun 2, 2016 at 0:33

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