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I've sampled a real world process, network ping times. The "round-trip-time" is measured in milliseconds. Results are plotted in a histogram:

enter image description here

Ping times have a minimum value, but a long upper tail.

I want to know what statistical distribution this is, and how to estimate its parameters.

Even though the distribution is not a normal distribution, I can still show what I am trying to achieve.

The normal distribution uses the function:

enter image description here

with the two parameters

  • μ (mean)
  • σ2  (variance)

Parameter estimation

The formulas for estimating the two parameters are:

alt text

Applying these formulas against the data I have in Excel, I get:

  • μ = 10.9558 (mean)
  • σ2  = 67.4578 (variance)

With these parameters I can plot the "normal" distribution over top my sampled data:

enter image description here

Obviously it's not a normal distribution. A normal distribution has an infinite top and bottom tail, and is symmetrical. This distribution is not symmetrical.


What principles would I apply, what flowchart, would I apply to determine what kind of distribution this is?

And cutting to the chase, what is the formula for that distribution, and what are the formulas to estimate its parameters?


I want to get the distribution so I can get the "average" value, as well as the "spread":

enter image description here

I am actually plotting the histrogram in software, and I want to overlay the theoretical distribution:

enter image description here

Tags: sampling, statistics, parameter-estimation, normal-distribution

  • 2
    Out of curiosity, have you tried asking this question on http://stats.stackexchange.com/ ? (I think your question is appropriate here as well, but you might get more/different answers there.)2010-08-05
  • 0
    i'll copy-pasta it there; me an my 1 rep.2010-08-05
  • 0
    My understanding is that there is a _large_ literature on stuff like network ping times and the answer is probably in a paper somewhere.2010-08-05
  • 2
    Have you tried to use http://ccsl.mae.cornell.edu/eureqa ?2010-08-06
  • 0
    [Link to the question on stats.stackexchange](http://stats.stackexchange.com/questions/1315).2010-08-06
  • 0
    @jug Eureqa looked like a great tool. But it's best guess is `f(x) = 1.000` and `f(y) = y`2010-08-06
  • 0
    Could someone remove the discrete-mathematics tag? This is clearly statistics - not what I associate with discrete mathematics.2010-08-12

4 Answers 4