From: Gavin Sinclair <gsinclair@...>
Date: 2004-08-15T12:52:12+09:00
Subject: Re: Random variable library?

On Sunday, August 15, 2004, 9:11:08 AM, Paul wrote:

>> Yes, but what about: "give me a normal distribution between 0 and 10"?
>> That probably doesn't make sense without some extra parameters, but
>> they can be defaults/derived.

> Don't take this personally, but this is where I start getting nervous.
> A normal distribution is characterized _entirely_ by its mean and 
> variance, and has an infinite range.  If what you want falls between 0
> and 10, then it ain't normal.

That's fine and understood.  I'm not looking for distributed random
numbers for probability analysis, just for node placement and cluster
sizes in a network simulation.  There's no scientific validity riding
on the values pumped out of the RNG.

To use the 0-10 example, if the distribution has mean 5 and std-dev 2,
then only a tiny portion of generated numbers will fall outside of
(0..10).  Those numbers are insignificant to me (not to others, I
appreciate), so I can just regenerate until I get a value I want.

That makes me realise: the "window" aspect of this (only seeing values
within a certain range) is a superficial operation that can be applied
seperately from any actual generation and distribution, with
themselves are two different layers.

>> Then I'd like to be able to bias it as well, if that makes sense.  So
>> you can have a "normal" distribution between 0 and 10, biased so that
>> the center is on 3 instead of 5.
>> 
>> IF that makes sense... :/

> Sorry, but no it doesn't.  The normal distribution is symmetric about
> its mean.  If you want an assymetric distribution (the term is "skewed",
> not "biased"), then once again it ain't normal.

So I have two choices: either apply a (0..10) window to a Normal(3,2)
distribution, or go and learn about asymmetric distributions.  (I
suspect you can have a plain "skewed distribution" applied to any
other distribution to get the result I want.)

> If you're going to do probability modeling, you need to understand the
> models or you're going to get in trouble.  Somebody already suggested
> Ross's book, I'll put in my 2-cents for taking a look at "Simulation
> Modeling and Analysis" by Law & Kelton.  It has a good review of prob &
> stats and a very comprehensive discussion of the theory and algorithms
> for random variate generation.

Like I said, I'm not doing probability modeling, but I'll still be
interested to read about these things in more detail.

> I know that usenet posts can come across as harsh, and that's not my
> intention.  Please accept this response as a strong caution rather than
> as a put-down.

Not at all; thanks very much for the input.  You've educated me and
helped to clarify my aims.

Gavin