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===The Exponential Distribution===
=== 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:
<br>
::<math>f(t)=\lambda {e}^{-\lambda(t-\gamma )}</math>


(also known as the two-parameter exponential in this form) with two parameters, namely <math>\lambda </math>  and  <math>\gamma .</math>
The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by: <br>
If the location parameter, <math>\gamma </math>, is assumed to be zero, the distribution then becomes the one-parameter exponential or,
<br>
::<math>f(t)=\lambda {{e}^{-\lambda t}}</math>


The exponential distribution and its characteristics are presented in more detail in Chapter [[The Exponential Distribution]].
::<span class="texhtml">''f''(''t'') = λ''e''<sup> − λ(''t'' − γ)</sup></span>
 
with two parameters, namely <span class="texhtml">λ</span> and <span class="texhtml">γ</span>&nbsp;(this form is also known as the two-parameter exponential). If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the&nbsp;distribution&nbsp;becomes the one-parameter exponential or, <br>
 
::<span class="texhtml">''f''(''t'') = λ''e''<sup> − λ''t''</sup></span>
 
The exponential distribution and its characteristics are presented in&nbsp;detail in&nbsp;the&nbsp;[[The Exponential Distribution|Exponential Distribution]]&nbsp;chapter.  


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Revision as of 20:08, 11 March 2012

The Exponential Distribution

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

f(t) = λe − λ(t − γ)

with two parameters, namely λ and γ (this form is also known as the two-parameter exponential). If the location parameter, γ, is assumed to be zero, then the distribution becomes the one-parameter exponential or,

f(t) = λe − λt

The exponential distribution and its characteristics are presented in detail in the Exponential Distribution chapter.


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