Template:Example: Lognormal General Example Complete Data

From ReliaWiki
Revision as of 23:45, 13 February 2012 by Harry Guo (talk | contribs)
Jump to navigation Jump to search

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]