[R] finding mean and SD for a log-normal distribution

[David Winsemius]

On May 16, 2012, at 6:37 AM, Andras Farkas wrote:

> Dear R Expert
>
> allow me to ask a quick qestion: I have a mean value of 6 and a SD  
> of 3 describing my distribution. I would like to "convert" this  
> distribution into a log normal distribution that would best describe  
> it when resimulated using log normal distribution. Currently I am  
> using another software to estimate the respective mean and SD on the  
> log scale and the results are: 1.6667 and SD 0.47071. Then, to best  
> reproduce my original distribution in R, I use the following commands:
>
> c <- rlnorm(5000,1.6667,0.47071)
> d <- exp(c)
> mean(c)
> sd(c)

I get a better match to those values with:
distrib <- rlnorm(500000,1.682,0.47071)

(Bad practice to use 'c' as an object name.)

>
> and the results for mean and SD are 5.92 and 2.94 (original 6 and  
> 3), respectively, which I am reasonably happy with. I would like to  
> grow independent of the another software I use, but am unable to  
> figure out how to generate the values of 1.6667 and 0.47071 using R.  
> could someone please help me with this question?

You need to review your resources on statistical distributions. The  
Wikipedia article has the needed transformations for parameters  
between the log and untransformed scales under the section entitled  
Arithmetic moments.

So that was the basis for this test:

# mu for LN
 > log(6) - 0.5*log(1+9/6^2)
[1] 1.680188
# sigma for LN
 > sqrt( log( 1 +9/6^2))
[1] 0.4723807
 > c <- rlnorm(500000,1.680188,0.4723807)
 > d <- exp(c)
# Expected value
 > mean(c)
[1] 5.99303
# SD
 > sd(c)
[1] 2.996532

So my half-assed approximation was in better agreement with theory  
than your "other software". On the other hand you haven't really given  
us much background for this estimation process so its not possible to  
offer a solid value judgment. R has package that do distribution  
fitting, MASS has fitdistr and there is a fitdistrplus package ....  
and others I believe. There's a monograph out about R's facilities but  
at the moment I cannot put my hands on my copy. There is a  
Distributions TaskView:
http://cran.r-project.org/web/views/Distributions.html

-- 

David Winsemius, MD
West Hartford, CT