Thread: Need formula for the expected value between two points in a lognormal distribution

I'd greatly appreciate any help with this insurance-related math question:

I have the average and the standard deviation of a set of claims ranging between $5,000 and $100,000. My data has no claims in it with values under $5,000 nor does it have any claims in it with values in excess of $100,000. If I'm willing to assume that the overall claim distribution is lognormal, how can I use the average and standard deviation for this limited set of data to derive the mu and sigma for the entire distribution?

Thanks in advance for any and all help!

- Steve J

Originally Posted by Steve_J

I'd greatly appreciate any help with this insurance-related math question:

I have the average and the standard deviation of a set of claims ranging between $5,000 and $100,000. My data has no claims in it with values under $5,000 nor does it have any claims in it with values in excess of $100,000. If I'm willing to assume that the overall claim distribution is lognormal, how can I use the average and standard deviation for this limited set of data to derive the mu and sigma for the entire distribution?

Thanks in advance for any and all help!

- Steve J

Hi Steve J,

The Wikipedia article on the log-normal distribution,

Log-normal distribution - Wikipedia, the free encyclopedia,

gives formulas for mu and sigma in terms of the distribution's mean and standard deviation.

Thanks for the reply. Unfortunately, Wikipedia only seems to provide information for the entire distribution, the distribution limited to some threshold value of X, and/or the distribution in excess of some value of X. I didn't see anything there about what to do if you need to estimate the mean between two values (i.e., where an upper and lower cap both apply).

Again, any additional help would be greatly appreciated.