Editing Exponential distribution (section)

==Random variate generation==
{{further|Non-uniform random variate generation}}

<!-- This section is linked from [[Gamma distribution]] -->
A conceptually very simple method for generating exponential [[variate]]s is based on [[inverse transform sampling]]: Given a random variate ''U'' drawn from the [[uniform distribution (continuous)|uniform distribution]] on the unit interval {{open-open|0, 1}}, the variate

<math display="block">T = F^{-1}(U)</math>

has an exponential distribution, where ''F''{{i sup|−1}} is the [[quantile function]], defined by

<math display="block">F^{-1}(p)=\frac{-\ln(1-p)}{\lambda}.</math>

Moreover, if ''U'' is uniform on (0, 1), then so is 1 − ''U''.  This means one can generate exponential variates as follows:

<math display="block">T = \frac{-\ln(U)}{\lambda}.</math>

Other methods for generating exponential variates are discussed by Knuth<ref>[[Donald E. Knuth]] (1998). ''[[The Art of Computer Programming]]'', volume 2: ''Seminumerical Algorithms'', 3rd edn. Boston: Addison–Wesley. {{ISBN|0-201-89684-2}}. ''See section 3.4.1, p. 133.''</ref> and Devroye.<ref name="Luc Devroye">Luc Devroye (1986). ''[http://luc.devroye.org/rnbookindex.html Non-Uniform Random Variate Generation]''. New York: Springer-Verlag. {{ISBN|0-387-96305-7}}. ''See [http://luc.devroye.org/chapter_nine.pdf chapter IX], section 2, pp. 392–401.''</ref>

A fast method for generating a set of ready-ordered exponential variates without using a sorting routine is also available.<ref name="Luc Devroye"/>