Template:Alta a-e.e-e

Eyring-Exponential
The $$pdf$$ of the 1-parameter exponential distribution is given by:


 * $$f(t)=\lambda \cdot {{e}^{-\lambda \cdot t}}$$

It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail here) is given by:


 * $$\lambda =\frac{1}{m}$$


 * thus:


 * $$f(t)=\frac{1}{m}\cdot {{e}^{-\tfrac{t}{m}}}$$

The Eyring-exponential model $$pdf$$  can then be obtained by setting  $$m=L(V)$$:


 * $$m=L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}$$

and substituting for $$m$$  in the exponential $$pdf$$ equation:


 * $$f(t,V)=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}\cdot t}}$$