Exponential-logarithmic distribution: Difference between revisions

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==Related distributions==

The EL distribution has been generalized to form the Weibull-logarithmic distribution.<ref>Ciumara, Roxana; Preda, Vasile (2009) [http://www.vgtu.lt/leidiniai/leidykla/ASMDA_2009/PDF/16_sec_081_Ciumara_The_Weibull.pdf "The Weibull-logarithmic distribution in lifetime analysis and its properties"]{{Dead link|date=August 2019 |bot=InternetArchiveBot |fix-attempted=yes }}. In: L. Sakalauskas, C. Skiadas and

E. K. Zavadskas (Eds.) [http://www.vgtu.lt/leidiniai/leidykla/ASMDA_2009/ ''Applied Stochastic Models and Data Analysis''] {{Webarchive|url=https://web.archive.org/web/20110518043330/http://www.vgtu.lt/leidiniai/leidykla/ASMDA_2009/ |date=2011-05-18 }}, The XIII International Conference, Selected papers. Vilnius, 2009 {{ISBN|978-9955-28-463-5}}</ref>

If ''X'' is defined to be the [[random variable]] which is the minimum of ''N'' independent realisations from an [[exponential distribution]] with rate parameter ''&beta;'', and if ''N'' is a realisation from a [[logarithmic distribution]] (where the parameter ''p'' in the usual parameterisation is replaced by {{nowrap|1=(1&nbsp;&minus;&nbsp;''p'')}}), then ''X'' has the exponential-logarithmic distribution in the parameterisation used above.