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,  <math>\lambda ,</math>  and the effect lambda has on the  <math>pdf</math> , reliability and failure rate functions.
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====Effects of  <math>\lambda </math>  on the pdf====
[[Image:ALTA4pdf.gif|thumb|center|400px|''Pdf'' plot of the exponential distribution.]]  
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:• The scale parameter is  <math>\tfrac{1}{\lambda }</math> .
:• As  <math>\lambda </math>  is decreased in value, the distribution is stretched out to the right, and as  <math>\lambda </math>  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. The only parameter it has is the failure rate,  <math>\lambda </math> .
:• The distribution starts at  <math>T=0</math>  at the level of  <math>f(T=0)=\lambda </math>  and decreases thereafter exponentially and monotonically as  <math>T</math>  increases, and is convex.
:• As  <math>T\to \infty </math> ,  <math>f(T)\to 0</math>.
:• This  <math>pdf</math>  can be thought of as a special case of the Weibull  <math>pdf</math>  with  <math>\beta =1</math> .
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[[Image:ALTA4reliabilityvstimeplot.gif|thumb|center|400px|Reliability plot of the exponential distribution.]]
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====Effects of  <math>\lambda </math>  on the Reliability Function====
:• The 1-parameter exponential reliability function starts at the value of 1 at  <math>T=0</math> . It decreases thereafter monotonically and is convex.
:• As  <math>T\to \infty </math> ,  <math>R(T\to \infty )\to 0</math>.
====Effects of  <math>\lambda </math>  on the Failure Rate Function====
 
The failure rate function for the exponential distribution is constant and it is equal to the parameter  <math>\lambda </math> .
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[[Image:ALTA4FRvsTP.gif|thumb|center|400px|Failure Rate plot of the exponential distribution.]]
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Latest revision as of 01:06, 16 August 2012

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