Identify the dominant inter-spike-event distribution

Determine which of the inverse-Gaussian, log-normal, Weibull, biexponential-mixture, or truncated-power-law distributions most accurately describes the inter-spike-event intervals of tunnel-current noise in the nearly commensurate charge-density-wave phase of 1T-TaS2.

Background

The authors fit seven candidate distributions to the inter-spike-event intervals measured on Mott-Hubbard domains and metallic domain walls at 25 mV and approximately 200 mV. Although the gamma distribution is rejected, the available data do not distinguish among five alternative heavy-tailed forms: inverse Gaussian, log-normal, Weibull, biexponential mixture, and truncated power law.

Because the accessible interval range spans only approximately one decade, these candidate distributions are mathematically near-degenerate and none achieves a decisive Akaike weight. The paper therefore reports the intervals as heavy-tailed and over-dispersed without assigning a specific distribution, leaving the dominant interval law unresolved.