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A Novel Approach to Probability

机译：一种新的概率方法

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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.
机译：当P个不可区分的球随机分布在L个可区分的盒子中，并考虑稠密系统时，我们的自然直觉告诉我们，平均球数为P / L的盒子具有最高的概率，而没有盒子是空的。但是实际上，空框的概率始终是最高的。该事实与稀疏系统（即气体中的能量分布）的区别在于，在稀疏系统中，平均值具有最高的可能性。在这里，我们显示出，当我们假设盒子中所有可能的球构型都具有相等概率的要求时，就可以得到一个逼真的“长尾巴”分布。当应用于稀疏系统时，这种形式主义收敛到首选平均值的分布。我们计算由此假设得出的一些分布，并获得自然界中大多数已知的分布，即：齐普夫定律，本福德定律，粒子能量分布等。这种新颖方法的进一步推广，不仅可以更好地预测选举，民意测验，竞争公司之间的市场份额分布等，而且还可以为普朗克的著名经验发现（光子的能量为hv）提供令人信服的概率解释。

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