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leo nidas
04-06-2010, 04:29 AM
Hi there,

I have a question regarding the log normal and normal distribution.

What I think is that if Y has a normal distribution then X=log(Y) has log normal.

Specifically in Wolfram: http://mathworld.wolfram.com/LogNormalDistribution.html is written about lognormal:

"A continuous distribution in which the logarithm of a variable has a normal distribution." which is a bit unclear: of what kind of variable?.

"In probability theory, a log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. If Y is a random variable with a normal distribution, then X = exp(Y) has a log-normal distribution; likewise, if Y is log-normally distributed, then log(Y) is normally distributed"

which is not the case I think.. Am I not correct?

So what is correc?

If Y is normal log(Y) is lognormal?
or
If Y is normal exp(Y) is lognormal?

If the correct is the first one then wiki is wrong?

BGM
04-06-2010, 05:40 AM
If Y is normal, then exp(Y) is lognormal.
Note the support of the Y is the set of real number
but the domain of logarithm function is just the set of positive real number
So log(Y) is not well defined

Both wikipedia and mathworld are correct.
"A continuous distribution in which the logarithm of a variable has a normal distribution."
This sentence means if X ~ lognormal, then lnX ~ Normal

Ksharp
04-06-2010, 09:11 AM
If Y is normal exp(Y) is lognormal

log(x) will have more benefit than x.