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

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(Created page with ''''Lognormal Distribution General Example Interval Data''' Determine the lognormal parameter estimates for the data given in Table below. {|align="center" border=1 cellspacing=1…')
 
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{|align="center" border=1 cellspacing=1  
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|colspan="3" style="text-align:center"| Table - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
|colspan="3" style="text-align:center"| Table 9.3- Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
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!Data point index
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::<math>\begin{align}
::<math>\begin{align}
   & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\  
   & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\  
  & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.18   
  & {{{\hat{\sigma' }}}}= & 0.18   
\end{align}</math>
\end{align}</math>


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::<math>\begin{align}
::<math>\begin{align}
   & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\  
   & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\  
  & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.17   
  & {{{\hat{\sigma' }}}}= & 0.17   
\end{align}</math>
\end{align}</math>


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::<math>\begin{align}
::<math>\begin{align}
   & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\  
   & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\  
  & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.21   
  & {{{\hat{\sigma' }}}}= & 0.21   
\end{align}</math>
\end{align}</math>

Revision as of 23:42, 13 February 2012

Lognormal Distribution General Example Interval Data

Determine the lognormal parameter estimates for the data given in Table below.

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]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\ & {{{\hat{\sigma' }}}}= & 0.18 \end{align} }[/math]


For rank regression on [math]\displaystyle{ X\ \ : }[/math]

[math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\ & {{{\hat{\sigma' }}}}= & 0.17 \end{align} }[/math]


For rank regression on [math]\displaystyle{ Y\ \ : }[/math]

[math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\ & {{{\hat{\sigma' }}}}= & 0.21 \end{align} }[/math]
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