Newsgroups: comp.lang.apl
Path: utzoo!utgpu!news-server.csri.toronto.edu!torsqnt!tmsoft!itcyyz!yrloc!hui
From: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Subject: Re: Statistical Functions in J
Message-ID: <1991May21.042804.21102@yrloc.ipsa.reuter.COM>
Reply-To: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Organization: Iverson Software Inc.
References: <1991May12.145907.19563@yrloc.ipsa.reuter.COM> <356@tslwat.UUCP>
Date: Tue, 21 May 91 04:28:04 GMT

Lou Kates writes:

> Nevertheless, I believe the key  concept here is not expectation,
> probability or  measure  but regression and projection. From this
> viewpoint the old APL's domino  operator (or regression operator)
> had it correct and the above suggestions are a step backwards.
 
> The mean    of  a  vector  V   is the  regression coefficient  of
> projecting  V onto a vector  of all ones. The space orthogonal to
> this vector of ones  is the deviation space and the length of the
> projection of  V onto  this  deviation  space   divided   by  the
> dimensionality of the deviation  space (which is  the length of V
> minus one) is the standard deviation.
 
I am puzzled.  How would a belief in regression and projection
instead of expectation as the key concept materially affect
the design of the primitives m., n., and s.?
 
There are many statistical functions worthy of inclusion in the
language.  We are adding the new functions mean, normalization, 
and cross product matrix; and assigning the cognate weighted mean, 
weighted normalization, and weighted cross product to the dyads 
of these functions seems both consistent and useful.  These new 
functions do not preclude adding other statistical functions in 
the future, nor do they affect the domino function or any other 
existing function.  Therefore, I would not characterize them 
as a backward step.

We would welcome suggestions for other statistical functions.

-----------------------------------------------------------------
Roger Hui
Iverson Software Inc., 33 Major Street, Toronto, Ontario  M5S 2K9
(416) 925 6096