Template:ExponentialDistribution

The Exponential Distribution

The exponential distribution is commonly used for components or systems exhibiting a constant failure rate and is defined in its most general case by:

[math]\displaystyle{ f(t)=\lambda {e}^{-\lambda(t-\gamma )} }[/math]

(also known as the two-parameter exponential in this form) with two parameters, namely [math]\displaystyle{ \lambda }[/math] and [math]\displaystyle{ \gamma . }[/math] If the location parameter, [math]\displaystyle{ \gamma }[/math], is assumed to be zero, the distribution then becomes the one-parameter exponential or,

[math]\displaystyle{ f(t)=\lambda {{e}^{-\lambda t}} }[/math]

The exponential distribution and its characteristics are presented in more detail in Chapter 7.