Template:Ald characteristics: Difference between revisions

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===Characteristics===
#REDIRECT [[Distributions_Used_in_Accelerated_Testing#The_Lognormal_Distribution]]
:* The lognormal distribution is a distribution skewed to the right.
:* The  <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.
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[[Image:chp4pdf.png|center|400px|''Pdf'' of the lognormal distribution.]]
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The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean <math>({{\overline{T}}^{\prime }})</math> and the log-std (<math>{{\sigma }_{{{T}'}}}</math>), and the effect they have on the <math>pdf</math>.
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'''Looking at the Log-Mean'''  <math>({{\overline{T}}^{\prime }})</math>
:* The parameter,  <math>\bar{{T}'}</math>, or the log-mean life, or the  <math>MTT{F}'</math> in terms of the logarithm of the  <math>{T}'s</math>  is also the scale parameter and a unitless number.
:* For the same  <math>{{\sigma }_{{{T}'}}}</math>  the  <math>pdf</math> 's skewness increases as  <math>\bar{{T}'}</math>  increases.
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[[Image:chp4pdf2.png|center|400px|''Pdf'' of the lognormal distribution with different log-mean values.]]
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====Looking at the Log-STD  <math>({{\sigma }_{{{T}'}}})</math>====
:* The parameter  <math>{{\sigma }_{{{T}'}}}</math>, or the standard deviation of the  <math>{T}'s</math>  in terms of their logarithm or of their  <math>{T}'</math>, is also the shape parameter, and not the scale parameter as in the normal  <math>pdf</math>. It is a unitless number and assumes only positive values.
:* The degree of skewness increases as  <math>{{\sigma }_{{{T}'}}}</math>  increases, for a given  <math>\bar{{T}'}</math>.
:* For  <math>{{\sigma }_{{{T}'}}}</math>  values significantly greater than 1, the  <math>pdf</math>  rises very sharply in the beginning (i.e., for very small values of  <math>T</math>  near zero), and essentially follows the ordinate axis, peaks out early, and then decreases sharply like an exponential  <math>pdf</math>  or a Weibull  <math>pdf</math>  with  <math>0<\beta <1</math>.
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[[Image:chp4pdf3.png|center|400px|''Pdf'' of the lognormal distribution with different log-std values.]]
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Latest revision as of 03:24, 16 August 2012

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