Editing Gumbel distribution (section)

===Occurrences of the discrete Gumbel distribution===
In [[combinatorics]], the discrete Gumbel distribution appears as a limiting distribution for the hitting time in the [[coupon collector's problem]]. This result was first established by [[Pierre-Simon de Laplace|Laplace]] in 1812 in his ''Théorie analytique des probabilités'', marking the first historical occurrence of what would later be called the Gumbel distribution.

In [[number theory]], the Gumbel distribution approximates the number of terms in a random [[partition of an integer]]<ref>{{cite journal |doi=10.1215/S0012-7094-41-00826-8 |title=The distribution of the number of summands in the partitions of a positive integer |year=1941 |last1=Erdös |first1=Paul |last2=Lehner |first2=Joseph |journal=Duke Mathematical Journal |volume=8 |issue=2 |pages=335}}</ref> as well as the trend-adjusted sizes of maximal [[prime gaps]] and maximal gaps between [[prime constellations]].<ref>{{cite journal |arxiv=1301.2242 |last=Kourbatov |first= A. |title=Maximal gaps between prime ''k''-tuples: a statistical approach |journal=Journal of Integer Sequences |volume=16 |year=2013|bibcode=2013arXiv1301.2242K }} Article 13.5.2.</ref>

In [[probability theory]], it appears as the distribution of the maximum height reached by discrete walks (on the lattice <math>{\mathbb N}^2</math>), where the process can be reset to its starting point at each step.<ref name=AguechAlthagafiBanderier/>

In [[analysis of algorithms]], it appears, for example, in the study of the maximum carry propagation in base-<math>b</math> addition algorithms.<ref>{{citation |title=The average time for carry propagation|year=1978|first1=Donald E.|last1=Knuth|journal=Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae|volume=81|pages=238–242}}</ref>