From: Stefaan Lhermitte <stefaan.lhermitte_at_biw.kuleuven.be>

Date: Fri 03 Jun 2005 - 20:16:28 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Jun 03 20:39:59 2005

Date: Fri 03 Jun 2005 - 20:16:28 EST

H = Si (Sj ( sqrt [ (Ai - Aj)² + (Bi - Bj)² ] ) )

where:

A, B = two vectors (with numerical data) of length n
sqrt = square root

Si = summation over i (= 0 to n) Sj = summation over j (= 0 to n) Ai = element of A with index i Aj = element of A with index j Bi = element of B with index i Bj = element of B with index j

n is not fixed, but it changes with every run for my program. Therefore for I am looking for a simplication of h in order to calculate it when my A and B get extendend by 1 element (n = n + 1).

I know a computional simplified formula exists for the standard deviation (sd) that is much easier in iterative programming. Therefore I wondered I anybody knew about analog simplifications to simplify H:

sd = sqrt [ ( Si (Xi - mean(X) )² ) /n ] -> simplified computation -> sqrt [ (n * Si( X² ) - ( Si( X ) )² )/ n² ]

This simplied formula is much easier in iterative programming, since I
don't have to keep every element of X.

E.g.: I have a vector X[1:10] and I already have caculated Si( X[1:10]²
) (I will call this A) and Si( X ) (I will call this B).
When X gets extendend by 1 element (eg. X[11]) it easy fairly simple to
calculate sd(X[1:11]) without having to reuse the elements of X[1:10].
I just have to calculate:

sd = sqrt [ (n * (A + X[11]²) - (A + X[11]²)² ) / n² ]

This is fairly easy in an iterative process, since before we continue
with the next step we set:

A = (A + X[11]²)

B = (B + X[11])

Can anybody help me to do something comparable for H? Any other help to calculate H easily in an iterative process is also welcome!

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Jun 03 20:39:59 2005

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