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)
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