Generate a truncated lognormal distribution given mean, variance, lower bound and upper bound? Basically, I would like to generate a sample of truncated lognormal distribution given mean, variance, lower bound and upper bound. Note that the mean and variance here are the mean and variance of the truncated lognormal distribution NOT the $\mu$ and $\sigma$.
I tried to find the underlying $\mu$ and $\sigma$ using the formula in the paper:
A Left and Right Truncated Lognormal Distribution for the Stars
Note that m = exp($\mu$) in this paper.
Basically I tried to solve the equation system of which the unknown variables are $\mu$ and $\sigma$:
1.Mean($\mu$, $\sigma$, $x_l$, $x_u$) = desired mean
2.Variance($\mu$, $\sigma$, $x_l$, $x_u$) = desired variance
But it seems that this equation could is too complicated for MATLAB to solve. I was wondering if there is a more efficient way to generate a truncated lognormal distribution given mean and variance?
Any help would be greatly appreciated!

Update: I have solved this question NUMERICALLY by optimization.
Basically, define a loss function:
loss = $(desired\ mean - F(\mu, \sigma, x_l, x_u))^2 + (desired\ std - G(\mu, \sigma, x_l, x_u))^2$
Where the function F and G is the analytical formula of mean and standard deviation of truncated lognormal distribution.
The formula was elaborated in the paper: Zaninetti
Minimizing this loss function could solve this problem numerically.
Thank you so much for the help!
