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| ===The Two-Parameter Exponential Distribution===
| | #REDIRECT [[The Exponential Distribution]] |
| The two-parameter exponential ''pdf'' is given by:
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| ::<math>f(T)=\lambda {{e}^{-\lambda (T-\gamma )}},f(T)\ge 0,\lambda >0,T\ge 0\text{ or }\gamma </math>
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| where <math>\gamma </math> is the location parameter.
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| Some of the characteristics of the two-parameter exponential distribution are [19]:
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| #The location parameter, <math>\gamma </math>, if positive, shifts the beginning of the distribution by a distance of <math>\gamma </math> to the right of the origin, signifying that the chance failures start to occur only after <math>\gamma </math> hours of operation, and cannot occur before.
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| #The scale parameter is <math>\tfrac{1}{\lambda }=\bar{T}-\gamma =m-\gamma </math>.
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| #The exponential <math>pdf</math> has no shape parameter, as it has only one shape.
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| #The distribution starts at <math>T=\gamma </math> at the level of <math>f(T=\gamma )=\lambda </math> and decreases thereafter exponentially and monotonically as <math>T</math> increases beyond <math>\gamma </math> and is convex.
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| #As <math>T\to \infty </math>, <math>f(T)\to 0</math>.
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| <br>
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| {{one parameter exp distribution}}
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