I am running a simulation. One of my parameters is sampled from a normal distribution. I would like to perform a sensitivity analysis using a right skewed distribution.
This is what I had hoped to do: specify a log normal distribution, with a leftward translation so that it has the same cumulative density below zero as the reference normal, and have the same mean and variance (on the log scale) as the reference normal.
I have played around with these parameters. I am stuck. 1) this is even possible? 2) if it is possible, I may need to solve for the parameters numerically... But I am having trouble specifying an equation(s). I am having trouble with the algebra
If it is impossible to have the exact same expectation, variance, and cumulative density below zero, I'd be happy with letting the variance be unconsteained.
Alternatively, I'd be happy using any right skewed distribution, I only started with the log normal because I thought it would be simple.
I can post the equations I have worked on, but I suspect they are not useful. I've been using the definitions posted at this link (http://www.mathworks.com/help/stats/lognpdf.html)