# Harmonic Interpolation

• Aug 12th 2009, 09:36 AM
Harmonic Interpolation
Hey folks.
I have to find the estimated limits of this distribution using harmonic interpolation and I have no idea how to do this.
Here's the table for the upper 25% points of my distribution. Could someone show me how its done please? I.e. Whats the limit of P as n goes to infinity.
Bleh having latex trouble so heres it set out not so well...

n ----- P
5 --- 0.5218
6 --- 0.5356
7 --- 0.5455
8 --- 0.5509
9 --- 0.5553
10 -- 0.5591
11 -- 0.5624
12 -- 0.5651
13 -- 0.5675
14 -- 0.5697
15 -- 0.5715
16 -- 0.5731
17 -- 0.5746
18 -- 0.5760
19 -- 0.5772
20 -- 0.5784
21 -- 0.5793
22 -- 0.5804
23 -- 0.5813
24 -- 0.5821
25 -- 0.5829
26 -- 0.5835
27 -- 0.5842
28 -- 0.5850
29 -- 0.5855
30 -- 0.5861
40 -- 0.5906
50 -- 0.5938
60 -- 0.5959
70 -- 0.5977
80 -- 0.5992
90 -- 0.6001
100 -- 0.6011
200 -- 0.6063
400 -- 0.6098
• Aug 15th 2009, 08:20 AM
Actually just realized its EXTRApolation I have to use. This help anyone..?
• Aug 15th 2009, 10:55 AM
Scoodai
unity is a limit
So you mean you are supposed to use 'extrapolation' rather than 'harmonic interpolation'? Or do you have to use 'harmonic extrapolation'?

It seems like a trick question. The P values are apparently cumulative probabilities. So if you're talking about the distribution over the values of n, then the value of P as n goes to infinity is just one, because that's true for all distributions.

Or are you talking about another distribution?
• Aug 15th 2009, 12:31 PM
Its a different distribution. Which I cant remember the name of! But basically... n is the sample size from the population, the P values are the upper 25% points of a distribution that has been made using a few millions runs (in Maple).
Maybe I'm using the wrong words here though...
I took an n-sized sample from the normal distribution N(0,1), did a few bits and bobs to it and came out with a a single value.
Then did this a few million times to get a few million values and found various percentage points of it.
But as I got to n=100 and higher my Maple program was taking 10+ hours to run so I cant really go much higher and obviously cant test n=infinity!
Might be extrapolation or harmonic extrapolation I'm unfamiliar with both so I'm not sure, alternatively if there's another way to do it that would be great too!
• Aug 15th 2009, 01:00 PM
Scoodai
more about the bits and bobs?
Oh, okay. It sounds like the P values are not probabilities at all, but rather upper quartiles from the distribution. And this distribution itself is a function of the value of n.

Can you say what the 'bit and bobs' were that you did to the samples from the normal distribution? In principle, using (generalized) convolutions you should be able to translate those operations that you did on the samples into an analytical result that you would get with infinitely many samples.

Without knowing these details, you could use a phenomenological approach. There are various extrapolation strategies that might be useful. For instance, if you plot 1/n on the abscissa and 1/P on the ordinate, your data are roughly linear. Or, at least they're not so embarrassingly nonlinear that no one would try to fit a Michaelis-Menten model to find the asymptote. See Michaelis?Menten kinetics - Wikipedia, the free encyclopedia.