I've sampled a real world process, network ping times. The "round-trip-time" is measured in milliseconds. Results are plotted in a histogram:
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:
with the two parameters
- μ (mean)
- σ2 (variance)
The formulas for estimating the two parameters are:
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:
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":
I am actually plotting the histrogram in software, and I want to overlay the theoretical distribution:
Tags: sampling, statistics, parameter-estimation, normal-distribution