Template:Two parameter exp distribution: Difference between revisions

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(Created page with '===The Two-Parameter Exponential Distribution=== The two-parameter exponential ''pdf'' is given by: ::<math>f(T)=\lambda {{e}^{-\lambda (T-\gamma )}},f(T)\ge 0,\lambda >0,T\ge 0…')
 
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#As <math>T\to \infty </math>, <math>f(T)\to 0</math>.
#As <math>T\to \infty </math>, <math>f(T)\to 0</math>.
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{{one parameter exp distribution}}

Revision as of 22:34, 16 January 2012

The Two-Parameter Exponential Distribution

The two-parameter exponential pdf is given by:

[math]\displaystyle{ f(T)=\lambda {{e}^{-\lambda (T-\gamma )}},f(T)\ge 0,\lambda \gt 0,T\ge 0\text{ or }\gamma }[/math]

where [math]\displaystyle{ \gamma }[/math] is the location parameter. Some of the characteristics of the two-parameter exponential distribution are [19]:

  1. The location parameter, [math]\displaystyle{ \gamma }[/math], if positive, shifts the beginning of the distribution by a distance of [math]\displaystyle{ \gamma }[/math] to the right of the origin, signifying that the chance failures start to occur only after [math]\displaystyle{ \gamma }[/math] hours of operation, and cannot occur before.
  2. The scale parameter is [math]\displaystyle{ \tfrac{1}{\lambda }=\bar{T}-\gamma =m-\gamma }[/math].
  3. The exponential [math]\displaystyle{ pdf }[/math] has no shape parameter, as it has only one shape.
  4. The distribution starts at [math]\displaystyle{ T=\gamma }[/math] at the level of [math]\displaystyle{ f(T=\gamma )=\lambda }[/math] and decreases thereafter exponentially and monotonically as [math]\displaystyle{ T }[/math] increases beyond [math]\displaystyle{ \gamma }[/math] and is convex.
  5. As [math]\displaystyle{ T\to \infty }[/math], [math]\displaystyle{ f(T)\to 0 }[/math].