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

Latest revision as of 07:54, 14 August 2012

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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 - 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 }}}_{{{T}'}}}= & 0.18
-\end{align}</math>
-For rank regression on  <math>X\ \ :</math>
-::<math>\begin{align}
-  & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
- & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.17
-\end{align}</math>
-For rank regression on  <math>Y\ \ :</math>
-::<math>\begin{align}
-  & {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
- & {{{\hat{\sigma }}}_{{{T}'}}}= & 0.21
-\end{align}</math>