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Math Help - Harmonic Interpolation

  1. #1
    Super Member Deadstar's Avatar
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    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
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  2. #2
    Super Member Deadstar's Avatar
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    Actually just realized its EXTRApolation I have to use. This help anyone..?
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  3. #3
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    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?
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  4. #4
    Super Member Deadstar's Avatar
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    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!
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  5. #5
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    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.
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