Template:Example: Lognormal General Example Complete Data: Difference between revisions
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(Created page with ''''Lognormal Distribution General Example Complete Data''' Determine the lognormal parameter estimates for the data given in Table 9.4. {|align="center" border=1 cellspacing=1 …') |
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|colspan="3" style="text-align:center"| Table 9.4 - Non-Grouped Data | |colspan="3" style="text-align:center"| Table 9.4 - Non-Grouped Times-to-Failure Data | ||
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!Data point index | !Data point index | ||
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::<math>\begin{align} | ::<math>\begin{align} | ||
& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ | & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ | ||
& {{{\hat{\sigma }}}_ | & {{{\hat{\sigma '}}}_}= & 1.10 | ||
\end{align}</math> | \end{align}</math> | ||
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::<math>\begin{align} | ::<math>\begin{align} | ||
& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ | & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ | ||
& {{{\hat{\sigma } | & {{{\hat{\sigma' }}}}= & 1.24 | ||
\end{align}</math> | \end{align}</math> | ||
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::<math>\begin{align} | ::<math>\begin{align} | ||
& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ | & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ | ||
& {{{\hat{\sigma } | & {{{\hat{\sigma' }}}}= & 1.36 | ||
\end{align}</math> | \end{align}</math> | ||
Revision as of 23:44, 13 February 2012
Lognormal Distribution General Example Complete Data
Determine the lognormal parameter estimates for the data given in Table 9.4.
| Table 9.4 - Non-Grouped Times-to-Failure Data | ||
| Data point index | State F or S | State End Time |
|---|---|---|
| 1 | F | 2 |
| 2 | F | 5 |
| 3 | F | 11 |
| 4 | F | 23 |
| 5 | F | 29 |
| 6 | F | 37 |
| 7 | F | 43 |
| 8 | F | 59 |
Solution
Using Weibull++, the computed parameters for maximum likelihood are:
- [math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ & {{{\hat{\sigma '}}}_}= & 1.10 \end{align} }[/math]
For rank regression on [math]\displaystyle{ X\ \ : }[/math]
- [math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ & {{{\hat{\sigma' }}}}= & 1.24 \end{align} }[/math]
For rank regression on [math]\displaystyle{ Y\ \ : }[/math]
- [math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ & {{{\hat{\sigma' }}}}= & 1.36 \end{align} }[/math]