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