MATLAB: Find the σ and the μ of the lognormal function, having 1st percentile and the 99th percentile

lognormal percentile sigma mu

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)

Best Answer

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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MATLAB: Show probabilities (-inf+inf, -3dev-3dev and so on….)

"Integrating pdf" and "probability ... in given level ranges" sounds like the teacher wants you to use the cdf to get the cumulative probability between a range of values. E.g., maybe this is what is being asked:

>> mu = 12.5;
>> sigma = 3.75;
>> pd = makedist('Normal','mu',mu,'sigma',sigma); % Make a Normal pdf
>> cdf(pd,inf) - cdf(pd,-inf) % the integrated probablility between -inf and +inf
ans =
     1
>> cdf(pd,mu+3*sigma) - cdf(pd,mu-3*sigma) % the integrated probablity between mu-3sigma and mu+3sigma
ans =
    0.9973

MATLAB: How to use lognrnd

It is common to say that X is lognormally distributed with parameters mu and sigma if it has the pdf

f(x) = 1/(x*sigma*sqrt(2*pi))*exp(-(log(x)-mu)^2/(2*sigma^2))

If you now calculate the pdf of log(X), you'll see that it equals

g(y) = 1/(sigma*sqrt(2*pi))*exp(-(y-mu)^2/(2*sigma^2))

Thus log(X) is normally distributed with parameters mu and sigma.

To calculate 10^6 random numbers from a lognormally distributed random variable with mean 14 and standard deviation 7, your code from above is correct.

Best Answer

Related Solutions

MATLAB: Show probabilities (-inf+inf, -3dev-3dev and so on….)

MATLAB: How to use lognrnd

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