Lognormal Standard Error What is the Standard Error of the Lognormal distribution? I am particularly interested in comparing two probabilities from the distribution. I have the two proportions based on experiments, in general these proportions follow a lognormal fit. 
The standard error of differences from a normal distribution is straightforward (I've seen one other version of this which I think can see on wikipedia):
$SE = \sqrt{\frac{p (1-p)}{n} + \frac{q (1-q)}{m}}$
where $p, q$ are probabilities and $n, m$ sample sizes, expected to be from a normally distributed sample.
How would this be extended to the lognormal?
Edit:
The basic idea is to learn if the difference between two probabilities would be significant or not. I don't think I'm expressing my question correctly as I'm not a strict statistician. 
 A: The variance of a lognormal is $[e^{σ^2}-1] e^{2(σ+μ)} $ where μ and σ are the mean and standard deviation parameters of the related normal distribution.  Now the maximum likelihood estimate of the lognormal variance would be obtained by plugging in the maximum likelihood estimates of μ and σ into the expression above for the variance. Call that estimate $V$.
The mean of the lognormal is $M = e^{μ+σ^2/2}$  and its mle would be obtained by plugging in the mles for μ and σ in its expression.  Call that estimate $E$.
The estimate of the standard error for the difference of the means would depend on what estimate you use for the mean.  If you use $E$ I think it would be complicated.
However if the ordinary sample means were used to estimate the population means for the lognormal distirbutions then standard error for those means would be the population standard deviation divided by $\sqrt{n}$ where $n$ is the sample size for the lognormal.  This could be estimated by$\sqrt{V/n}$.  So if we compared means for the lognormal by their sample mean difference the standard error of the estimate would be $\sqrt{(V_1/n_1+V_2/n_2)}$ where $V_1$ and $V_2$ are the respective mles for the lognormal variances for populations 1 and 2 respectively and $n_1$ and $n_2$ are the corresponding sample sizes taken from populations 1 and 2.
