I suppose I don't get the point of this. That is, why don't you just use the harmonic mean?
I need help in the following:
I have the average of N numbers (say D1 , D2 , D3 .... , Dn).
I.e., I have (D1 + D2 + D3 + ... + D4) / N
but I don't have the numbers themselves
I want to approximate:
1/D1 + 1/D2 + 1/D3 + 1/D4 ... + 1/Dn
(1/D1 + 1/D2 + 1/D3 + 1/D4 ... + 1/Dn) / N
I don't have the distribution of these numbers, I could assume it as a normal distribution.
What is the best approximation as the number N becomes large?
Thanks for the reply.
My problem is that I have the arithmetic mean, but I don't have the actual numbers, I need a way to calculate 1/d1 + 1/d2 ....
I can get the actual numbers, but I need to run my experiments again which will take several days. When I ran the experiments I only recorded the average of the outputs, It was later that I realized that what I want is different.
I have read about the harmonic mean, it equals n / Y where Y is what I am looking for. the number n is available for me. Is there a way to calculate (in approximation) the harmonic mean given the arithmetic mean?
Last edited by Yacoub Massad; 05-18-2010 at 01:24 AM.
If you have the sample variance estimate ,
(by recording along with your sample mean estimate ),
you may try the taylor expansion:
In your case,
And then replace and by their corresponding estimate, we have
If you do not have and only have ,
one way is to take the zero order approximation only, i.e.
which is not accurate in general
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