Uneven Variance

I have a problem where i'm trying to characterize a system that has several independent variables. Each of these variables has an associated variance. What i'm doing is running a system model with a monte carlo analysis and trying to determine the overall variance on a system variable. I know the variances on all of the independent variables and for the most part they have a normal distribution. However, a few of them have a skewed distribution. For example, say the mean for one variable is 80 and the plus 3-sigma is 84 but the minus 3-sigma is 70. What kind of distribution do i use to model this? I looked at the log-normal distribution, but i'm having difficulty applying this to my problem. I hope this makes sense.


Does anyone have any suggestions?

You don't get to pick. It is what it is. The distribution of the independent variables will dictate the shape of your total distribution. Use your best Monte Carlo skills to develop a picture of the distribution. It wil NOT necessarily be anything that is well studied in the literature.