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'''Lognormal Distribution General Example Complete Data'''
#REDIRECT [[The Lognormal Distribution]]
 
Determine the lognormal parameter estimates for the data given in the following table.
{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"| 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>\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
& {\hat{\sigma '}}= & 1.10 
\end{align}</math>
 
For rank regression on  <math>X</math> 
 
::<math>\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
& {{{\hat{\sigma' }}}}= & 1.24 
\end{align}</math>
 
For rank regression on  <math>Y:</math> 
 
::<math>\begin{align}
  & {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
& {{{\hat{\sigma' }}}}= & 1.36 
\end{align}</math>

Latest revision as of 07:55, 14 August 2012

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