Exponential-logarithmic distribution: Difference between revisions

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{{Wikify|date=August 2009}}

In probability theory and statistics, the '''Exponentialexponential-Logarithmiclogarithmic (EL) distribution''' is a family of lifetime distribution with

decreasing failure rate, defined on the interval <math>&nbsp;(0,\infty&nbsp;&infin;)</math>. This distribution is parameterized by two parameters <math>p\in(0,1)</math> and <math>\beta >0</math>.

is a family of lifetime distribution with<br>

decreasing failure rate, defined on the interval <math>(0,\infty)</math>. This distribution is parameterized by two

parameters <math>p\in(0,1)</math> and <math>\beta >0</math>.

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== Introduction ==

The study of lengths of organisms, devices, materials, etc., is of major importance in the biological and engineering science. In general, life time of an device is expected to exhibit decreasing failure rate (DFR) when its behavior over time is characterized by 'work-hardening' (in engineering term) or 'immunity' (in biological term).

The study of length of organisms, devices,

materials, etc., is of major importance in the biological and

engineering science. In general, life time of an device is

expected to exhibit decreasing failure rate (DFR) when its

behavior over time is characterized by 'work-hardening' (in

engineering term) or 'immunity' (in biological term).

The Exponentialexponential-Logarithmiclogarithmic model together with its various properties are studied in Tahmasbi and Rezaei (2008)<ref>Tahmasbi, R., Rezaei, S., 2008, "A two-parameter lifetime distribution with decreasing failure rate", Computational Statistics and Data Analysis, Vol. 52, pp. 3889-3901.</ref>

Tahmasbi and Rezaei (2008)<ref>Tahmasbi, R., Rezaei, S., 2008, "A two-parameter lifetime distribution with decreasing failure rate", Computational Statistics and Data Analysis, Vol. 52, pp. 3889-3901.</ref>

This model is obtained under the concept of population heterogeneity (through the process of

compounding).