Transform Mean and standard deviation that follow normal distribution into Mi and Sigma that follow Logarithmic normal distribution (Log-Normal)
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As the title described, I have a problem with reliability with Mean Time To Repair (MTTR) with Mean = 550 e Standard derivation = 27 hours (Normal distribution). But, The maintenance is better represented as a Lognormal distribution and not Normal Distribution.
How can I convert Mi and Standart Derivation used into Normal Distribution to use it in Lognormal distribution.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/191757/image.png)
Cheers
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Jeff Miller
2018-7-10
finalmu = 550;
finalsigma = 27;
lnsigma = sqrt( log( finalsigma^2 / finalmu^2 + 1) );
lnmu = log( finalmu/exp(0.5*lnsigma^2) );
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Jeff Miller
2018-7-12
> the mean of the second plot isn't the variable "lnmu" that is 6.3087.
This is because the lognormal distribution is a transformation of a normally distributed variable. Specifically, if X is normal, then Y=exp(X) has a lognormal distribution. (That is, the distribution of log(Y) is normal.) In your case, the mean of X is 6.3087. But you are plotting the distribution of Y, and its mean is closer to exp(6.3087)--not exactly the same because exp() is a nonlinear transformation.
If you plotted X=log(Y), then you would see a normal with mean 6.3087 as I guess you are expecting.
I am not sure about the earlier equations. They are not the same, but maybe the earlier s was variance rather than standard deviation?
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