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Suppose I have a frequency distribution of some process of f_n(x) that is based on n samples, with n < N. I want to know the frequency distribution f_N(x) for N samples. The process was in n timesteps, and what I want to do is use the same distribution for a larger number of timesteps. The timesteps for both timeseries are the same.

Is it correct to just scale f_n by a factor N/n, so that I get

f_N(x) = N/n f_n(x)

What is the reasoning behind it?

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  • $\begingroup$ Are the timesteps smaller (i.e. faster sampling over an equivalent time period) or are they the same (i.e same sampling rate over a longer period)? $\endgroup$ – MikeP Oct 10 '14 at 15:06
  • $\begingroup$ They're the same. I updated the question. $\endgroup$ – jjack Oct 10 '14 at 15:10
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Yes, I think you can scale frequency distribution from the smaller sample. The reasoning is essentially an assumption that the process is stationary (http://en.wikipedia.org/wiki/Stationary_process).

You could also create confidence intervals for each range bin about the scaled average, but the mean or expected value for each would indeed be simply the scaled version exactly as you describe.

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  • $\begingroup$ Why would I want to use confidence intervals on each range bin? Is that to account for quantization effects and to account for sample time variation? $\endgroup$ – jjack Oct 10 '14 at 17:39
  • $\begingroup$ Just for randomness. Assuming there is some stationary probability of each sample landing in each bin, then you will have a range based on any finite number of samples. $\endgroup$ – MikeP Oct 10 '14 at 20:40
  • $\begingroup$ If I have a continuous distribution function with a good fit on the data, then I don't have to do that, or do I? $\endgroup$ – jjack Oct 11 '14 at 14:04

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