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We present exact expressions for the sum of states of noninteracting classical and quantum particles occupying a finite number of modes with arbitrary spacings. Exploiting a probabilistic analogy, we derive an analytic fourth-order approximation to the density of states, which captures its variance and kurtosis, and is superior to the previous, commonly used methods for all three particle statistics. Our approach employs a simple exact method of calculating the moments of the microcanonical density of states for quantum particles, which requires less computational effort than the commonly used saddle-point approximation. We test our methods numerically and discuss their applicability to various physical systems. [ABSTRACT FROM AUTHOR]

The article presents a comment on the study titled ``Excitons in Molecular Aggregates with Lévy-Type Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra''. The authors have calculated a substitute expansion and blueshift of the absorption band which they differentiated with an earlier evaluated Gaussian and Lorentzian case. The classification offers supplementary peaks in the absorption spectrum which is low and can obliterate any HWHM scaling appearing in disarray.