Template:Example: Lognormal General Example Complete Data - Revision history

Chris Kahn: Redirected page to The Lognormal Distribution

2012-08-14T07:55:26Z

Redirected page to The Lognormal Distribution

← Older revision		Revision as of 07:55, 14 August 2012
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	REDIRECT [[The Lognormal Distribution]]		#REDIRECT [[The Lognormal Distribution]]

Chris Kahn: Replaced content with 'REDIRECT The Lognormal Distribution'

2012-08-14T07:55:13Z

Replaced content with 'REDIRECT The Lognormal Distribution'

← Older revision		Revision as of 07:55, 14 August 2012
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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>~~

Richard House at 04:52, 8 August 2012

2012-08-08T04:52:01Z

← Older revision		Revision as of 04:52, 8 August 2012
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	'''Lognormal Distribution General Example Complete Data'''		'''Lognormal Distribution General Example Complete Data'''

	Determine the lognormal parameter estimates for the data given in the following ~~Table~~.		Determine the lognormal parameter estimates for the data given in the following table.
	{\|align="center" border=1 cellspacing=1		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\|colspan="3" style="text-align:center"\| ~~Table -~~ Non-Grouped Times-to-Failure Data		\|colspan="3" style="text-align:center"\| Non-Grouped Times-to-Failure Data
	\|-		\|-
	!Data point index		!Data point index
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	& {\hat{\sigma '}}= & 1.10		& {\hat{\sigma '}}= & 1.10
	\end{align}</math>		\end{align}</math>


	For rank regression on <math>X</math>		For rank regression on <math>X</math>
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	& {{{\hat{\sigma' }}}}= & 1.24		& {{{\hat{\sigma' }}}}= & 1.24
	\end{align}</math>		\end{align}</math>


	For rank regression on <math>Y:</math>		For rank regression on <math>Y:</math>

Harry Guo at 17:04, 2 March 2012

2012-03-02T17:04:12Z

← Older revision		Revision as of 17:04, 2 March 2012
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	'''Lognormal Distribution General Example Complete Data'''		'''Lognormal Distribution General Example Complete Data'''

	Determine the lognormal parameter estimates for the data given in Table ~~9.4~~.		Determine the lognormal parameter estimates for the data given in the following Table.
	{\|align="center" border=1 cellspacing=1		{\|align="center" border=1 cellspacing=1
	\|-		\|-
	\|colspan="3" style="text-align:center"\| Table ~~9.4~~ - Non-Grouped Times-to-Failure Data		\|colspan="3" style="text-align:center"\| Table - Non-Grouped Times-to-Failure Data
	\|-		\|-
	!Data point index		!Data point index

Harry Guo at 23:45, 13 February 2012

2012-02-13T23:45:55Z

← Older revision		Revision as of 23:45, 13 February 2012
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	For rank regression on <math>X~~\ \ :~~</math>		For rank regression on <math>X</math>

	::<math>\begin{align}		::<math>\begin{align}

Harry Guo at 23:45, 13 February 2012

2012-02-13T23:45:28Z

← Older revision		Revision as of 23:45, 13 February 2012
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	For rank regression on <math>Y~~\ \~~ :</math>		For rank regression on <math>Y:</math>

	::<math>\begin{align}		::<math>\begin{align}

Harry Guo at 23:45, 13 February 2012

2012-02-13T23:45:10Z

← Older revision		Revision as of 23:45, 13 February 2012
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	::<math>\begin{align}		::<math>\begin{align}
	& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\		& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
	& {{{\hat{\sigma '}~~}}_~~}= & 1.10		& {\hat{\sigma '}}= & 1.10
	\end{align}</math>		\end{align}</math>

Harry Guo at 23:44, 13 February 2012

2012-02-13T23:44:37Z

← Older revision		Revision as of 23:44, 13 February 2012
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	{\|align="center" border=1 cellspacing=1		{\|align="center" border=1 cellspacing=1
	\|-		\|-
	\|colspan="3" style="text-align:center"\| Table 9.4 - Non-Grouped Data ~~for Example 12~~		\|colspan="3" style="text-align:center"\| Table 9.4 - Non-Grouped Times-to-Failure Data
	\|-		\|-
	!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 }}}_~~{{{T}'}}~~}= & 1.10		& {{{\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 }~~}}_{{{T}'~~}}}= & 1.24		& {{{\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 }~~}}_{{{T}'~~}}}= & 1.36		& {{{\hat{\sigma' }}}}= & 1.36
	\end{align}</math>		\end{align}</math>

Harry Guo: 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 …'

2012-02-13T18:58:34Z

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 …'

New page

'''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
|-
|colspan="3" style="text-align:center"| 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>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 1.10
\end{align}</math>

For rank regression on <math>X\ \ :</math>

::<math>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 1.24
\end{align}</math>

For rank regression on <math>Y\ \ :</math>

::<math>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 2.83 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 1.36
\end{align}</math>