TITLE:
A Novel Approach to Probability
AUTHORS:
Oded Kafri
KEYWORDS:
Probability, Statistics, Benford’s Law, Zipf’s Law, Planck’s Law, Configurational Entropy
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.4,
March
24,
2016
ABSTRACT: When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system , our natural intuition
tells us that the box with the average number of balls P/L has the highest probability and that
none of boxes are empty; however in reality, the probability of the empty box is
always the highest. This fact is with contradistinction to sparse system (i.e. energy distribution in gas) in which the average value has the highest probability.
Here we show that when we postulate the requirement that all possible configurations
of balls in the boxes have equal probabilities, a realistic “long tail” distribution
is obtained. This formalism when applied for sparse systems converges to distributions
in which the average is preferred. We calculate some of the distributions resulted
from this postulate and obtain most of the known distributions in nature, namely:
Zipf’s law, Benford’s law, particles energy distributions, and more. Further generalization
of this novel approach yields not only much better predictions for elections, polls,
market share distribution among competing companies and so forth, but also a compelling
probabilistic explanation for Planck’s famous empirical finding that the energy
of a photon is hv.