Editing Erlang distribution (section)

===Other applications===

The age distribution of [[cancer]] [[Disease incidence|incidence]] often follows the Erlang distribution, whereas the shape and scale parameters predict, respectively, the number of [[Carcinogenesis|driver events]]  and the time interval between them.<ref>{{cite journal |last1=Belikov |first1=Aleksey V. |title=The number of key carcinogenic events can be predicted from cancer incidence |journal=Scientific Reports |date=22 September 2017 |volume=7 |issue=1 |page=12170 |doi=10.1038/s41598-017-12448-7|pmc=5610194 |pmid=28939880 |bibcode=2017NatSR...712170B }}</ref><ref>{{Cite journal|last1=Belikov|first1=Aleksey V.|last2=Vyatkin|first2=Alexey|last3=Leonov|first3=Sergey V.|date=2021-08-06|title=The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers|journal=PeerJ|language=en|volume=9|pages=e11976|pmid=34434669| doi=10.7717/peerj.11976| pmc=8351573|issn=2167-8359|doi-access=free}}</ref> More generally, the Erlang distribution has been suggested as good approximation of cell cycle time distribution, as result of multi-stage models.<ref>{{cite journal  |last1=Yates |first1=Christian A. |title=A Multi-stage Representation of Cell Proliferation as a Markov Process |journal=Bulletin of Mathematical Biology |date=21 April 2017 |volume=79 |issue=1 |doi=10.1007/s11538-017-0356-4 |pages=2905–2928|doi-access=free |pmid=29030804 |pmc=5709504 }}</ref><ref>{{cite journal  |last1=Gavagnin |first1=Enrico |title=The invasion speed of cell migration models with realistic cell cycle time distributions |journal=Journal of Theoretical Biology |date=21 November 2019 |volume=481 |doi=10.1016/j.jtbi.2018.09.010|arxiv=1806.03140 |pages=91–99 |pmid=30219568 |bibcode=2019JThBi.481...91G }}</ref>

The [[kinesin]] is a molecular machine with two "feet" that "walks" along a filament. The waiting time between each step is exponentially distributed. When [[green fluorescent protein]] is attached to a foot of the kinesin, then the green dot visibly moves with Erlang distribution of k = 2.<ref>{{Cite journal |last1=Yildiz |first1=Ahmet |last2=Forkey |first2=Joseph N. |last3=McKinney |first3=Sean A. |last4=Ha |first4=Taekjip |last5=Goldman |first5=Yale E. |last6=Selvin |first6=Paul R. |author1-link=Ahmet Yıldız (scientist) |author4-link=Taekjip Ha |author6-link=Paul R. Selvin  |date=2003-06-27 |title=Myosin V Walks Hand-Over-Hand: Single Fluorophore Imaging with 1.5-nm Localization |url=https://www.science.org/doi/10.1126/science.1084398 |journal=Science |language=en |volume=300 |issue=5628 |pages=2061–2065 |doi=10.1126/science.1084398 |pmid=12791999 |bibcode=2003Sci...300.2061Y |issn=0036-8075}}</ref>

It has also been used in marketing for describing interpurchase times.<ref>{{cite journal |first1=C. |last1=Chatfield |first2=G.J. |last2=Goodhardt |title=A Consumer Purchasing Model with Erlang Interpurchase Times |journal=Journal of the American Statistical Association |date=December 1973 |volume=68 |issue=344 |pages=828–835 |doi=10.1080/01621459.1973.10481432 }}</ref>