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

Chris Kahn: Redirected page to The Lognormal Distribution

2012-08-14T07:54:20Z

Redirected page to The Lognormal Distribution

← Older revision		Revision as of 07:54, 14 August 2012
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	~~'''Lognormal Distribution General Example Interval Data'''~~		#REDIRECT [[The_Lognormal_Distribution]]

	~~Determine the lognormal parameter estimates for the data given in the table below.~~
	~~{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"~~
	\|-
	~~\|colspan="3" style="text-align:center"\| Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)~~
	\|-
	~~!Data point index~~
	~~!Last Inspected~~
	~~!State End Time~~
	\|-
	~~\|1 \|\|30\|\|32~~
	\|-
	~~\|2 \|\|32\|\|35~~
	\|-
	~~\|3 \|\|35\|\|37~~
	\|-
	~~\|4 \|\|37\|\|40~~
	\|-
	~~\|5 \|\|42\|\|42~~
	\|-
	~~\|6 \|\|45\|\|45~~
	\|-
	~~\|7\|\|50\|\|50~~
	\|-
	~~\|8\|\|55\|\|55~~
	\|}

	~~'''Solution'''~~

	~~This is a sequence of interval times-to-failure where the intervals vary substantially in length. Using Weibull++, the computed parameters for maximum likelihood are calculated to be:~~

	~~::<math>\begin{align}~~
	~~& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\~~
	~~& {{{\hat{\sigma' }}}}= & 0.18~~
	~~\end{align}</math>~~

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

	~~::<math>\begin{align}~~
	~~& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\~~
	~~& {{{\hat{\sigma' }}}}= & 0.17~~
	~~\end{align}</math>~~

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

	~~::<math>\begin{align}~~
	~~& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\~~
	~~& {{{\hat{\sigma' }}}}= & 0.21~~
	~~\end{align}</math>~~

Richard House at 04:50, 8 August 2012

2012-08-08T04:50:49Z

← Older revision		Revision as of 04:50, 8 August 2012
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	'''Lognormal Distribution General Example Interval Data'''		'''Lognormal Distribution General Example Interval Data'''

	Determine the lognormal parameter estimates for the data given in ~~Table~~ below.		Determine the lognormal parameter estimates for the data given in the table below.
	{\|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 Data Times-to-Failure with intervals (lnterval and left censored)		\|colspan="3" style="text-align:center"\| Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
	\|-		\|-
	!Data point index		!Data point index
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	& {{{\hat{\sigma' }}}}= & 0.18		& {{{\hat{\sigma' }}}}= & 0.18
	\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' }}}}= & 0.17		& {{{\hat{\sigma' }}}}= & 0.17
	\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

2012-03-02T17:04:28Z

← Older revision		Revision as of 17:04, 2 March 2012
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	{\|align="center" border=1 cellspacing=1		{\|align="center" border=1 cellspacing=1
	\|-		\|-
	\|colspan="3" style="text-align:center"\| Table 3- Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)		\|colspan="3" style="text-align:center"\| Table - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
	\|-		\|-
	!Data point index		!Data point index

Harry Guo at 17:03, 2 March 2012

2012-03-02T17:03:26Z

← Older revision		Revision as of 17:03, 2 March 2012
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	{\|align="center" border=1 cellspacing=1		{\|align="center" border=1 cellspacing=1
	\|-		\|-
	\|colspan="3" style="text-align:center"\| Table 9.3- Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)		\|colspan="3" style="text-align:center"\| Table 3- Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
	\|-		\|-
	!Data point index		!Data point index

Harry Guo at 23:42, 13 February 2012

2012-02-13T23:42:39Z

← Older revision		Revision as of 23:42, 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 - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)		\|colspan="3" style="text-align:center"\| Table 9.3- Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
	\|-		\|-
	!Data point index		!Data point index
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	::<math>\begin{align}		::<math>\begin{align}
	& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\		& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
	& {{{\hat{\sigma }~~}}_{{{T}'~~}}}= & 0.18		& {{{\hat{\sigma' }}}}= & 0.18
	\end{align}</math>		\end{align}</math>

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	::<math>\begin{align}		::<math>\begin{align}
	& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\		& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
	& {{{\hat{\sigma }~~}}_{{{T}'~~}}}= & 0.17		& {{{\hat{\sigma' }}}}= & 0.17
	\end{align}</math>		\end{align}</math>

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	::<math>\begin{align}		::<math>\begin{align}
	& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\		& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
	& {{{\hat{\sigma }~~}}_{{{T}'~~}}}= & 0.21		& {{{\hat{\sigma' }}}}= & 0.21
	\end{align}</math>		\end{align}</math>

Harry Guo: Created page with ''''Lognormal Distribution General Example Interval Data''' Determine the lognormal parameter estimates for the data given in Table below. {|align="center" border=1 cellspacing=1…'

2012-02-13T18:56:52Z

Created page with ''''Lognormal Distribution General Example Interval Data''' Determine the lognormal parameter estimates for the data given in Table below. {|align="center" border=1 cellspacing=1…'

New page

'''Lognormal Distribution General Example Interval Data'''

Determine the lognormal parameter estimates for the data given in Table below.
{|align="center" border=1 cellspacing=1
|-
|colspan="3" style="text-align:center"| Table - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
|-
!Data point index
!Last Inspected
!State End Time
|-
|1 ||30||32
|-
|2 ||32||35
|-
|3 ||35||37
|-
|4 ||37||40
|-
|5 ||42||42
|-
|6 ||45||45
|-
|7||50||50
|-
|8||55||55
|}

'''Solution'''

This is a sequence of interval times-to-failure where the intervals vary substantially in length. Using Weibull++, the computed parameters for maximum likelihood are calculated to be:

::<math>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.18
\end{align}</math>

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

::<math>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.17
\end{align}</math>

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

::<math>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.21
\end{align}</math>