From: phil colbourn <philcolbourn_at_gmail.com>

Date: Sun, 04 May 2008 23:15:24 +1000

Date: Sun, 04 May 2008 23:15:24 +1000

Thank you for your reply.

I think I have a poor understanding of this distribution but, if I understand your answer albeit roughly, then to get a mean of 100 I need to select a mu and derive the sd using sqrt(2*(log(100)-mu)).

That helps a lot.

My application is in modeling/simulating failure/repair processes which I have read are typically log-normal. I should now be able to get the result i expect to get.

Thanks again.

On Sun, May 4, 2008 at 3:11 PM, Berwin A Turlach <berwin_at_maths.uwa.edu.au> wrote:

> G'day Phil,

*>
**> On Sun, 4 May 2008 14:05:09 +1000
**> phil colbourn <philcolbourn_at_gmail.com> wrote:
**>
**> > rlnorm takes two 'shaping' parameters: meanlog and sdlog.
**> >
**> > meanlog would appear from the documentation to be the log of the
**> > mean. eg if the desired mean is 1 then meanlog=0.
**>
**> These to parameters are the mean and the sd on the log scale of the
**> variate, i.e. if you take the logarithm of the produced numbers then
**> those values will have the given mean and sd.
**>
**> If X has an N(mu, sd^2) distribution, then Y=exp(X) has a log-normal
**> distribution with parameters mu and sd.
**>
**> R> set.seed(1)
**> R> y <- rlnorm(10000, mean=3, sd=2)
**> R> summary(log(y))
**> Min. 1st Qu. Median Mean 3rd Qu. Max.
**> -4.343 1.653 2.968 2.987 4.355 10.620
**> R> mean(log(y))
**> [1] 2.986926
**> R> sd(log(y))
**> [1] 2.024713
**>
**>
**> > I noticed on wikipedia lognormal page that the median is exp(mu) and
**> > that the mean is exp(mu + sigma^2/2)
**> >
**> > http://en.wikipedia.org/wiki/Log-normal_distribution
**>
**> Where mu and sigma are the mean and standard deviation of a normal
**> variate which is exponentiated to obtain a log normal variate. And
**> this holds for the above example (upto sampling variation):
**>
**> R> mean(y)
**> [1] 143.1624
**> R> exp(3+2^2/2)
**> [1] 148.4132
**>
**> > So, does this mean that if i want a mean of 100 that the meanlog
**> > value needs to be log(100) - log(sd)^2/2?
**>
**> A mean of 100 for the log-normal variate? In this case any set of mu
**> and sd for which exp(mu+sd^2/2)=100 (or mu+sd^2/2=log(100)) would do
**> the trick:
**>
**> R> mu <- 2
**> R> sd <- sqrt(2*(log(100)-mu))
**> R> summary(rlnorm(10000, mean=mu, sd=sd))
**> Min. 1st Qu. Median Mean 3rd Qu. Max.
**> 4.010e-04 1.551e+00 7.075e+00 1.006e+02 3.344e+01 3.666e+04
**> R> mu <- 4
**> R> sd <- sqrt(2*(log(100)-mu))
**> R> summary(rlnorm(10000, mean=mu, sd=sd))
**> Min. 1st Qu. Median Mean 3rd Qu. Max.
**> 0.9965 25.9400 56.0200 101.2000 115.5000 3030.0000
**> R> mu <- 1
**> R> sd <- sqrt(2*(log(100)-mu))
**> R> summary(rlnorm(10000, mean=mu, sd=sd))
**> Min. 1st Qu. Median Mean 3rd Qu. Max.
**> 9.408e-05 4.218e-01 2.797e+00 8.845e+01 1.591e+01 7.538e+04
**>
**> Note that given the variation we would expect in the mean in the last
**> example, the mean is actually "close enough" to the theoretical value
**> of 100:
**>
**> R> sqrt((exp(sd^2)-1)*exp(2*mu + sd^2)/10000)
**> [1] 36.77435
**>
**> HTH.
**>
**> Cheers,
**>
**> Berwin
**>
**> =========================== Full address =============================
**> Berwin A Turlach Tel.: +65 6515 4416 (secr)
**> Dept of Statistics and Applied Probability +65 6515 6650 (self)
**> Faculty of Science FAX : +65 6872 3919
**> National University of Singapore
**> 6 Science Drive 2, Blk S16, Level 7 e-mail: statba_at_nus.edu.sg
**> Singapore 117546 http://www.stat.nus.edu.sg/~statba<http://www.stat.nus.edu.sg/%7Estatba>
**>
*

-- Phil " Someone else has solved it and posted it on the internet for free " [[alternative HTML version deleted]] ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Sun 04 May 2008 - 13:20:38 GMT

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