On the apparently fixed dispersion of size distributions

TL;DR

The paper investigates why size distributions of clusters often appear fixed and explores how assumptions about distribution types influence this perception, highlighting the need for careful statistical modeling.

Contribution

It reveals that the perceived fixed dispersion results from fitting data with log-normal or exponential functions, suggesting alternative approaches are necessary.

Findings

Distribution widths are comparable to mean sizes.

Fitting with specific functions can mask true variability.

Alternative statistical models are proposed.

Abstract

Probability density functions (PDF) of statistical distributions of cluster sizes N, where N is the number of particles in the cluster, often seem to have less freedom than expected from considering the number of degrees of freedom at the clusters' source. The full width at half maximum appears to be comparable to the average <N>. Such a hidden symmetry is intriguing theoretically and practically impairs size selection towards narrow distributions. However, reviewing the example of Helium cluster beams demonstrates that the origin of the apparent fixing is the assumption that the distributions should be log-normal or exponential and the subsequent use of these functions to fit the data in n = ln(N) log-space. This demands more care when using parametric statistics. Alternatives to the traditionally employed fitting functions are discussed.