[EMAIL PROTECTED] (Jay Warner) wrote in message news:<[EMAIL PROTECTED]>... > We can anticipate that "weeks to fill a position" will be Poisson > distribtured - they can't get less than 0, and could stretch out > considerable. A.k.a., log-Normal distributed if you count fractions of > weeks.
This is wrong on all sorts of levels. "Time to some event" when discretised, would rarely, if ever, be approximately Poisson. I have never seen anything even close. "Number of events per unit time" is sometimes approximately Poisson, implying an exponentially distributed time-to-event. When discretised, that's going to be geometric, /not/ Poisson. Add to that, the Poisson is not in any sense a discrete equivalent of the lognormal. For example, the variance of the Poisson is proportional to the mean, while the variance of the lognormal is proportional to the square of the mean. > Use of an _average_ for this data will give extra weight to those long > to fill positions, No, it will give equal weight to all positions, at least in the sense that the ordinary average is a weighted average with all weights equal. It's not clear what you mean. > and possibly distort the reported value - making it > "mean" less to the receiver. "distort" in what sense? Leaving aside censoring issues for the moment (which would affect things the opposite direction anyway), if you're estimating the population mean, the sample mean is an unbiased (though not alway particularly efficient) estimator. > The core problem is that when we read "average" we often think in terms > of a Normal distribution, and expect the data to cluster near that > average. A Poisson dist. doesn't cluster there, so the meaning of > 'average' isn't what the reader thinks it is. Er, it does. The mode is always very close to the parameter for a Poisson; it can't be more that one lattice-step away. Glen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
