Posts Tagged ‘normal curve’

October 20, 2010

Central Limit Theorem

A nice illustration of the Central Limit Theorem by convolution.

in R:

Heaviside <- function(x) {      ifelse(x>0,1,0) }
HH <- convolve( Heaviside(x), rev(Heaviside(x)),        type = "open"   )
HHHH <- convolve(HH, rev(HH),   type = "open"   )
HHHHHHHH <- convolve(HHHH, rev(HHHH),   type = "open"   )
etc.

What I really like about this dimostrazione is that it’s not a proof, rather an experiment carried out on a computer.

This empiricism is especially cool since the Bell Curve, 80/20 Rule, etc, have become such a religion.

NERD NOTE:  Which weapon is better, a 1d10 longsword, or a 2d4 oaken staff? Sometimes the damage is written as 1-10 longsword and 2-8 quarterstaff. However, these ranges disregard the greater likelihood of the quarterstaff scoring 4,5,6 damage than 1,2,7,8. The longsword’s distribution 1d10 ~Uniform[1,10], while 2d4 looks like a Λ.

(To see this another way, think of the combinatorics.)

(A Lévy-Pareto process has infinite variance.) comptes_rendus_28 Cauchy distribution has infinite variance as contrasted to… Gaussian distribution which shoots down REAL fast: fast.

August 26, 2010

original Mandelbrot article on cotton prices as a Levy process