Exponential-logarithmic distribution: Difference between revisions

Revision as of 12:21, 17 March 2011

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=== Distribution ===

The [[probability density function]] (pdf) of the EL distribution is given by{{cn}]}

:<math> f(x; p, \beta) := \left( \frac{1}{-\ln p}\right) \frac{\beta(1-p)e^{-\beta x}}{1-(1-p)e^{-\beta x}} </math>

where <math>p\in (0,1)</math> and <math>\beta >0</math>. This function is strictly decreasing in <math>x</math> and tends to zero as <math>x\rightarrow \infty</math>. The EL distribution has its [[mode|modal value]] given,of the density at x=0, given by

:<math>\frac{\beta (1-p)}{-p \ln p}</math>

The EL reduces to the [[exponential distribution]] with rate parameter <math>\beta</math>, as <math>p\rightarrow 1</math>.

The [[cumulative distribution function]] is given by