Template:Example: Normal General Example All Data Type: Difference between revisions

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'''Normal Distribution General Example All Data Type'''
#REDIRECT[[Normal_Distribution_Examples#Times-to-Failure_with_All_Types_of_Censored_Data]]
 
Suppose our data set includes left and right censored, interval censored and complete data as shown in the following table.
 
{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
!colspan="5" style="text-align:center"| Grouped Data Times-to-Failure with Suspensions and Intervals (Interval, Left and Right Censored)
|-
!Data point index
!Number in State
!Last Inspection
!State (S or F)
!State End Time
|-
|1 ||1 ||10 ||F||10
|-
|2 ||1 ||20 ||S||20
|-
|3 ||2 ||0  ||F||30
|-
|4 ||2 ||40 ||F||40
|-
|5 ||1 ||50 ||F||50
|-
|6 ||1 ||60 ||S||60
|-
|7 ||1 ||70 ||F||70
|-
|8 ||2 ||20 ||F||80
|-
|9 ||1 ||10 ||F||85
|-
|10||1 ||100||F||100
|}
 
 
'''Solution'''
 
This data set can be entered into Weibull++ by selecting the data type Times to Failure, with Right Censored Data (Suspensions), with Interval and Left Censored Data and with Grouped Observations.
 
The computed parameters using maximum likelihood are:
 
::<math>\begin{align}
  & \widehat{\mu }= & 48.11 \\
& {{{\hat{\sigma }}}_{T}}= & 26.42 
\end{align}</math>
 
For rank regression on x:
 
::<math>\begin{align}
  & \widehat{\mu }= & 49.99 \\
& {{{\hat{\sigma }}}_{T}}= & 30.17 
\end{align}</math>
 
For rank regression on y:
 
::<math>\begin{align}
  & \widehat{\mu }= & 51.61 \\
& {{{\hat{\sigma }}}_{T}}= & 33.07 
\end{align}</math>

Latest revision as of 05:44, 14 August 2012

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