[RC5] Stats suggestion

Pyke, David David.Pyke at CIBC.com
Fri Jan 5 15:04:53 EST 2001


The math is right, you just may want to start the average with their total
average at the X day point. (i.e., start they 30 day weighted average with
their unweighted average at their 30th day)

It would be less confusing for the participants who aren't privy to this
discussion...



> -----Original Message-----
> From: Ben Clifford [mailto:benc at hawaga.org.uk]
> Sent: Friday, January 05, 2001 2:43 PM
> To: rc5 at lists.distributed.net
> Subject: Re: [RC5] Stats suggestion
> 
> 
> 
> On Fri, 5 Jan 2001 bwilson at fers.com wrote:
> 
> > It sounds like there would be a somewhat complex "catch-up" 
> process to get
> > all the averages into place.
> 
> Not complex - just long winded. You just run through time fast:
> Something like:
> 
> avg = 0
> for day = 0 to today
> 	avg = k1 * history[day] + k2 * avg
> end-for
> 
> > Do you have a formula handy for calculating k1 and k2 to 
> obtain a given
> > half-life?
> 
> Yes. It is pretty simple, I just couldn't remember it off the 
> top of my
> head so I wrote k1 and k2  which I defined to be the correct values,
> rather than posting some other incorrect formulae. I'm sure 
> you can tell I
> am a pedant/mathematician :-)
> 
> new_avg = K * old_avg + (1-K) * new avg
> 
> K can be any value between 0 and 1 - the larger the value, 
> the longer the
> half-life.
> 
> Scratching away on a bit of paper, I think that:
> 
> let i be the number of periods in the half life. ie. if you 
> are performing
> an iteration every day, as I believe is happening at the 
> moment, then a
> 7-day half life would have i=7
> 
> Then
> 
> K = 0.5 ^ ( 1 / i)
> 
> where ^ is "to the power of"
> 
> So a half life of 7 days should have K=0.905723 approx.
> and 30 days should have K=0.977159 approx.
> 
> The arithmetic can be done floating or fixed point - the 
> linux kernel does
> it in fixed point. If you want, I can cut the relevant bit of 
> code (in C)
> out for you to look at (it is in sched.c and sched.h off the top of my
> head).
> 
> I would be grateful if some other mathematicians on the list 
> would check
> the above and find the stupid mistakes I have probably made.
> 
> Ben
> 
> -- 
> http://www.hawaga.org.uk/travel/ for my rotating world map applet
> http://www.hawaga.org.uk/benc_key.txt PGP / GPG key 
> 0x30F06950 - please use it!
> 
> 
> 
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