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| ===The Two-Parameter Exponential Distribution===
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| 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 [[Appendix: Weibull References|
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| [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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