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Thanks Toni. Yes I agree that rejection and resampling affects the variance (also the mean), but it will often suffice for the purpose in hand. I agree, too, that the gamma can be useful (it can be almost any shape). Your practical advice about <Constant + sample> seems reasonable enough to me - but then I've never travelled on a narrow boat, I'm too impatient. MP > -----Original Message----- > From: Toni Roome [SMTP:[log in to unmask]] > Sent: 19 April 1999 11:16 > To: 'Caroline Collins ' > Cc: [log in to unmask] > Subject: RE: Discrete Event Simulation - Log-Normal Distribution > > Hi Caroline, > > you wrote: > > > In the model random numbers for the service procedure are generated > > using > > > the inverse transformation method, to create 'a day in the life' of the > > lock > > > system. I inititally modelled the lock procedure(service) using the > > Normal > > > distribution, as it fits this distribution. However on occasions, due > > to > > > high variance, there is a small chance that negative values can be > > produced. > > > This is clearly not acceptable as it cannot take minus 0.5 minutes for a > > > boat to enter a lock. In view of constraint I have now chosen > > Log-Normal > > > because it is closely related to the Normal distribution, but is also is > > a > > > positive and positively skewed distribution. > > > > > > Has anyone else used a Log-Normal distribution to describe length of > > service > > > in a simulation model. Can anyone offer more information on this > > > distribution as there appears to be very little written about it, > > compared > > > to the Normal. > > > Although based on the normal the lognormal is signifiicantly skewed, which > may on may not be a feature of the problem. > > If you want a distribution which is also is likely to mimic the normal then, > apart from the truncation method which Mike suggests (and which actually > then underestimates the variance), why not use a Gamma distribution? > > Gamma distributions can approximate normal distributions when the shape > parameter is high, and they are always non-negative. If the likelIhood of > the value being truncated is small (mean > 2-3 standard deviations from > zero) then they will be similar. > > From what I know about canal boats (having holidayed on them for several > years) there is in fact likely to be a significant minimum value for time > for a boat to enter a lock - ever if it was nosed up to the lock gates to > start with, if you use any of the distributions as given then you will > generate impossibly small values unless you allow for this. > > Similar physical considerations also apply to time ot fill/emplty the lock > and for a boat ot exit. > > You probably need a model: > time to enter: = constant + postive skewed distribution > > where the distribution might well be a Gamma or Log-normal. > > If you have some actual data (even mean and standard deviation) then once > you can come up with a minimum figure which should be subtracted from the > mean you can then estimate the parameters of your distribution. > > regards, > -- > Toni Roome > Senior Lecturer in Statistics and OR > Pathway leader MSc. Decision Sciences > > "One should each day, try to hear a little song, > read a good poem, see a fine picture, and, if it is > possible, speak a few reasonable words" (Goethe) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%