find the σ and the μ of the lognormal function, having 1st percentile and the 99th percentile

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SYML2nd
SYML2nd on 21 Nov 2019
Commented: SYML2nd on 21 Nov 2019
I have to build find the σ and the μ of the lognormal function, having the value of the 1st percentile (which is 30) and the 99th percentile (which is 60).
Do you have any suggestion to do it simply with matlab
Thank you in advance (be nice, I am not a statistic guru, I have already tried to solve it by myself searching a lot in statistic book)
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Accepted Answer

the cyclist
the cyclist on 21 Nov 2019
First you need to understand the math problem, then you can use MATLAB to solve numerically.
You can find the CDF of the lognormal distribution in this wikipedia section. So, you'll have two simultaneous equations (each equation is a function of σ and μ):
  • Eq 1: cdf of the lognormal at 30 = 0.01
  • Eq 2: cdf of the lognormal at 60 = 0.99
This is two equations in two unknowns, and with bit of manipulation, I believe can make this two linear equations in two unknowns.
Since this seems like homework, I think maybe that's enough of a hint to get you going.
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