This band shape is described by the function:
where

is the mean band position,

is the half band width at half maximum, and

is the
frequency distribution function.
Source:
PAC, 1996, 68, 2223
(Glossary of terms used in photochemistry (IUPAC Recommendations 1996))
on page 2252
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by
A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).
XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic,
J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
https://doi.org/10.1351/goldbook.