Lognormal with negative mean? I have a set of cycle time data for a processing counter. Since the cycle time is less than 1 minute, so the time taken are all less than 1 (ie 0.14m).  I am trying to fit a distribution, but result shown by STATFIT (software) was LOGNORMAL DISTRIBUTION with negative mean value. Is this possible?
 A: The log-normal distribution is defined only for positive values. Because of the relationship between the log-normal and the normal distribution, i.e., if $X$ is log-normal, then $\log X$ is normal, the log-normal distribution is often parametrised by the parameters for the corresponding normal distribution, for which the mean value parameter may be negative. Most likely, your software returns these parameters.
The mean of the log-normal distribution is $e^{\mu+\sigma^2/2}$, where $\mu$ and $\sigma^2$ are the mean and variance of the corresponding normal distribution.
A: I expect what actually happened is that the estimate of the $\mu$ parameter was negative, but for the lognormal $\mu$ is not the mean. It's the mean of the log of that random variable, which can be negative.

Alternatively, if you really do mean that the fitted mean was negative:
It might be possible for a shifted lognormal - like a lognormal distribution, but with an additional parameter representing a shift of the whole distribution. This is sometimes called a three-parameter lognormal.
An alternative might be a flipped lognormal, one flipped about 0.
So while its not possible for an ordinary two paramater lognormal, there are things that are like lognormals and related to them, that might apply.
