ALTA ALTA Standard Folio Data Eyring-Exponential

From ReliaWiki
Revision as of 21:52, 10 February 2012 by Nicolette Young (talk | contribs)
Jump to navigation Jump to search
Webnotes-alta.png
Standard Folio Data Eyring-Exponential
ALTA

The [math]\displaystyle{ pdf }[/math] of the 1-parameter exponential distribution is given by:
[math]\displaystyle{ f(t)=\lambda \cdot {{e}^{-\lambda \cdot t}} }[/math]
It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by:
[math]\displaystyle{ \lambda =\frac{1}{m} }[/math]
thus:
[math]\displaystyle{ f(t)=\frac{1}{m}\cdot {{e}^{-\tfrac{t}{m}}} }[/math]
The Eyring-exponential model [math]\displaystyle{ pdf }[/math] can then be obtained by setting [math]\displaystyle{ m=L(V) }[/math] in Eqn. (eyring):
[math]\displaystyle{ m=L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]
and substituting for [math]\displaystyle{ m }[/math] in Eqn. (pdfexpm2):
[math]\displaystyle{ f(t,V)=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}\cdot t}} }[/math]

Get More Details...



Docedit.png