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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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| <br>
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| ====Effects of <math>\lambda </math> on the pdf====
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| [[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> .
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| :• 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.
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| :• 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> .
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| :• 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.
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| :• As <math>T\to \infty </math> , <math>f(T)\to 0</math>.
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| :• 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====
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| :• The 1-parameter exponential reliability function starts at the value of 1 at <math>T=0</math> . It decreases thereafter monotonically and is convex.
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| :• As <math>T\to \infty </math> , <math>R(T\to \infty )\to 0</math>.
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| Effects of <math>\lambda </math> on the Failure Rate Function
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| The failure rate function for the exponential distribution is constant and it is equal to the parameter <math>\lambda </math> .
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| <br>
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| [[Image:ALTA4FRvsTP.gif|thumb|center|400px|Failure Rate plot of the exponential distribution.]]
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