Template:Example: Lognormal General Example Interval Data

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Lognormal Distribution General Example Interval Data

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

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]