The Nature and Correlation of Random Distributions

The ordered patterns of random distributions in many different fields are examined from the viewpoint of an experimental physicist relying on measured facts. By reversing the traditional graphics, that is, by plotting logarithm of frequency against an additive variate scale, the complete pattern can be traced with far greater discrimination. No indisputable evidence has so far been found for the existence of the Gaussian or 'normal' distribution. The general pattern appears as a hyperbola, the exponential asymptotes of which intersect at a value of the logarithm of frequency, ln q, dependent on the arbitrarily chosen interval of measurement. A different but synonymous representation of the same reality is obtained by choosing a different interval. The arbitrariness is removed in a new way by a change of interval such that the asymptotes intersect at the certainty ln q = 0, i.e. unit probability. The two transformed asymptotes are then represented by the two independent exponentials q = C^y'_1 and q = C^y'_2. When and only when this transformation is made, the mode frequency value is predictable in terms of the bases C_1 and C_2 which thereby define the distribution in absolute terms and so, for the first time, allow random distributions in different fields to be correlated. The bases C_1 and C_2 appear as the respective chances of an independent interval or step taken along the variate towards smaller and larger values. The evidence suggests, intriguingly, that Nature restricts the mean chance C to the narrow range 0.5 to 0.2, where 0.5 is the even-chance value.