Template:Example: Lognormal General Example Interval Data: Difference between revisions

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'''Lognormal Distribution General Example Interval Data'''
#REDIRECT [[The_Lognormal_Distribution]]
 
Determine the lognormal parameter estimates for the data given in Table below.
{|align="center" border=1 cellspacing=1
|-
|colspan="3" style="text-align:center"| Table 9.3- Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
|-
!Data point index
!Last Inspected
!State End Time
|-
|1 ||30||32
|-
|2 ||32||35
|-
|3 ||35||37
|-
|4 ||37||40
|-
|5 ||42||42
|-
|6 ||45||45
|-
|7||50||50
|-
|8||55||55
|}
 
'''Solution'''
 
This is a sequence of interval times-to-failure where the intervals vary substantially in length. Using Weibull++, the computed parameters for maximum likelihood are calculated to be:
 
::<math>\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
& {{{\hat{\sigma' }}}}= & 0.18 
\end{align}</math>
 
 
For rank regression on  <math>X\ \ :</math> 
 
::<math>\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
& {{{\hat{\sigma' }}}}= & 0.17 
\end{align}</math>
 
 
For rank regression on  <math>Y\ \ :</math> 
 
::<math>\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
& {{{\hat{\sigma' }}}}= & 0.21 
\end{align}</math>

Latest revision as of 07:54, 14 August 2012

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