On 20/07/11 21:08, Simon Knapp wrote:
Hi All,
This is not really an R question but a statistical one. If someone could
either give me the brief explanation or point me to a reference that might
help, I'd appreciate it.
I want to estimate the mean of a log-normal distribution, given the (log
scale normal) parameters mu and sigma squared (sigma2). I understood this
should simply be:
exp(mu + sigma2)
I think you meant exp(mu + sigma2/2); that's what you used below
(and that's what the right answer is.
... but I the following code gives me something strange:
R<- 10000000
mu<- -400
sigma2<- 200
tmp<- rlnorm(R, mu, sqrt(sigma2)) # a sample from the desired log-normal
distribution
muh<- mean(log(tmp))
sigma2h<- var(log(tmp))
#by my understanding, all of the the following vectors should then contain
very similar numbers
c(mu, muh)
c(sigma2, sigma2h)
c(exp(mu + sigma2/2), exp(muh + sigma2h/2), mean(tmp))
I get the following (for one sample):
c(mu, muh)
[1] -400.0000 -400.0231
c(sigma2, sigma2h)
[1] 200.0000 199.5895
c(exp(mu + sigma2/2), exp(muh + sigma2h/2), mean(tmp))
[1] 5.148200e-131 4.097249e-131 5.095888e-150
so they do all contain similar numbers, with the exception of the last
vector, which is out by a factor of 10^19. Is this likely to be because one
needs **very** large samples to get a reasonable estimate of the mean... or
am I missing something?
This is in effect an FAQ.
You seem to be missing an understanding of floating point arithmetic.
All of the last three values that you display are ***zero*** to all
practical
intents and purposes.
Experiment with some values where you are not dealing with exp(-300)
if you want to gain some insight into the log normal distribution.
cheers,
Rolf Turner
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