Template:Two parameter exp distribution

The Two-Parameter Exponential Distribution
The two-parameter exponential pdf is given by:


 * $$f(t)=\lambda {{e}^{-\lambda (t-\gamma )}},f(t)\ge 0,\lambda >0,t\ge 0\text{ or }\gamma $$

where $$\gamma $$ is the location parameter. Some of the characteristics of the two-parameter exponential distribution are [19]:
 * 1) The location parameter, $$\gamma $$, if positive, shifts the beginning of the distribution by a distance of $$\gamma $$ to the right of the origin, signifying that the chance failures start to occur only after $$\gamma $$ hours of operation, and cannot occur before.
 * 2) The scale parameter is $$\tfrac{1}{\lambda }=\bar{t}-\gamma =m-\gamma $$.
 * 3) The exponential $$pdf$$ has no shape parameter, as it has only one shape.
 * 4) The distribution starts at $$t=\gamma $$ at the level of $$f(t=\gamma )=\lambda $$ and decreases thereafter exponentially and monotonically as $$t$$ increases beyond $$\gamma $$ and is convex.
 * 5) As $$t\to \infty $$, $$f(t)\to 0$$.