Template:Characteristics of the exponential distribution alta: Difference between revisions

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=== Characteristics  ===
#REDIRECT [[Distributions_Used_in_Accelerated_Testing#Characteristics_of_the_Exponential_Distribution]]
 
The characteristics of the 1-parameter exponential distribution can be exemplified by examining its parameter, lambda (<span class="texhtml">λ<span style="font-family: sans-serif;">)</span></span> and the effect lambda has on the ''pdf'', reliability and failure rate functions.<br>
 
==== Effects of <span class="texhtml">λ</span> on the ''pdf''  ====
 
<br>
 
[[Image:ALTA4pdf.png|center|400px]] <br>
 
:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .
:*As <span class="texhtml">λ</span> is decreased in value, the distribution is stretched out to the right, and as <span class="texhtml">λ</span> is increased, the distribution is pushed toward the origin.
:*This distribution has no shape parameter, as it has only one shape (i.e., the exponential). Its only parameter is the failure rate, <span class="texhtml">λ</span> .
:*The distribution starts at <span class="texhtml">''T'' = 0</span> at the level of <span class="texhtml">''f''(''T'' = 0) = λ</span>. It decreases thereafter exponentially and monotonically as <span class="texhtml">''T''</span> increases, and it is convex.
:*As <math>T\to \infty </math> , <math>f(T)\to 0</math>.
:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.
 
<br> [[Image:ALTA4reliabilityvstimeplot.png|center|400px]] <br>
 
==== Effects of <span class="texhtml">λ</span> on the Reliability Function  ====
 
:*The 1-parameter exponential reliability function starts at the value of 1 at <span class="texhtml">''T'' = 0</span> . It decreases thereafter monotonically and is convex.
:*As <math>T\to \infty </math> , <math>R(T\to \infty )\to 0</math>.
 
==== Effects of <span class="texhtml">λ</span> on the Failure Rate Function  ====
 
The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .
 
<br> [[Image:ALTA4FRvsTP.png|center|400px]] <br>

Latest revision as of 01:06, 16 August 2012

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