Template:Example: Lognormal General Example Complete Data

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Lognormal Distribution General Example Complete Data

Determine the lognormal parameter estimates for the data given in Table 9.4.

Table 9.4 - Non-Grouped Data for Example 12
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 }}}_{{{T}'}}}= & 1.10 \end{align} }[/math]


For rank regression on [math]\displaystyle{ X\ \ : }[/math]

[math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ & {{{\hat{\sigma }}}_{{{T}'}}}= & 1.24 \end{align} }[/math]


For rank regression on [math]\displaystyle{ Y\ \ : }[/math]

[math]\displaystyle{ \begin{align} & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\ & {{{\hat{\sigma }}}_{{{T}'}}}= & 1.36 \end{align} }[/math]