I came across this interesting video the other day:
Also see:
I was curious and did some googling to find out more. The video mentions Eugene Wigner who first came up with the fucntion with regard to Random Matrix Theory. Apparently, it was later adjusted slightly and also given the name the Guassian Orthogonal Ensemble and also used in Quantum Chaos Theory.
Here's the equation for the function on wikipedia:
(look under the section for "Distribution of Level Spacings")
Wolfram seemed to have the same essential equation labelled as the WignerSurmise of the Gaussian Orthogonal Ensemble:
I googled some more and found some attempts to apply this to financial data. The function was always used in the same way, as an attempt to better tweak a portfolio of stocks by determining if they were well correlated. Here is an example:
However, i was more curious as to the mean and standard deviation of the distribution plot.
I took the function and plugged it into Google and it gave me an active graph:
I decided to get an approximation of the mean using ten y values corresponding to ten x values from 0 to 3.0 after which the y value is zero to two decimal spaces.
Interestingly, the corresponding x value or mean level spacing turned out to be 1.613 which is pretty damn close to the golden ratio of 1.618, especially if you take into account I only sampled ten values to two decimal places!
I did try and figure out the standard deviation, and found it to be .276, but I'm not sure I did that correctly. If I did, plus and minus one standard deviation did not correspond to anything exciting on the x-axis that I could see but I may have messed that up. I'm just an amateur at this kind of stuff, so professionals are welcome to help out!
Anyway, just posting this to share and let others check my work and maybe throw in their own ideas.
p.s. -- this was not posted with the intent to prove anything about fibs, and I'm not saying it does, although if the mean is correct its pretty interesting that it is approximate to the Golden Ratio. My intention was actually to find a universal pattern that was not fib related. lol
Here's a pic with the mean values:
By the way I'm pretty sure I got the mean right because here's somebody else's result: