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About
There is an interesting link between probability distributions and orthogonal polynomials. For instance, consider the Hermite polynomials, H0,H1,…. These are orthogonal with respect to the weight function e−x2/2 on the support (−∞,∞). In other words, ∫∞−∞Hi(x)Hj(x)e−x2/2dx=2π−−√i!δij.
The weighting function and the coefficient having a factor 2π−−√ should ring a bell; specifically, you find these represented in a standard normal distribution.
Norbert Wiener recognized that the two are intricately linked and developed what is called the Gauss-Hermite Polynomial Chaos. In short, we can write a random variable k of any distribution as an infinite series about a random variable ζ of a normal (Gaussian) distribution by using the Hermite polynomials as basis functions:
k=∑i=0∞kiHi(ζ).
It turns out, you can generalize this to other distributions, and to discrete distributions.
http://
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Operating location
Highsec
0.0%
Combat
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0
Ships lost
7
Danger rating
0%
ISK efficiency
0.0%
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EU
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Combat profile
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0.00B
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0.79B
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0%
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0.0%
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0.0
Ship class breakdown
Capsule
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3
Exhumer
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2
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Details
Founded
Mar 23, 2014
Founded by
Voxell
HQ
Structure #60000001
Tax rate
0.0%
War eligible
No
Primary timezone
US East
Primary location
Highsec
Last active
201407