Loglogistic Distribution Example - Revision history

Lisa Hacker at 21:39, 18 September 2023

2023-09-18T21:39:11Z

← Older revision		Revision as of 21:39, 18 September 2023
Line 1:		Line 1:
	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[The_Loglogistic_Distribution#General_Examples\|~~Life ~~Data Analysis Reference book]~~]''.</noinclude>		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude>

	Determine the loglogistic parameter estimates for the data given in the following table.		Determine the loglogistic parameter estimates for the data given in the following table.

Richard House at 17:51, 26 September 2012

2012-09-26T17:51:49Z

← Older revision		Revision as of 17:51, 26 September 2012
Line 4:		Line 4:
	Determine the loglogistic parameter estimates for the data given in the following table.		Determine the loglogistic parameter estimates for the data given in the following table.

	<center><math>\overset{{}}{\mathop{\text{Test data}}}\,</math></center>		<center><math>\overset{{}}{\mathop{\text{Test data}}}\,\,\!</math></center>

	<center><math>\begin{matrix}		<center><math>\begin{matrix}
Line 18:		Line 18:
	\text{9} & \text{675} & \text{680} \\		\text{9} & \text{675} & \text{680} \\
	\text{10} & \text{884} & \text{889} \\		\text{10} & \text{884} & \text{889} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>


Line 26:		Line 26:
	& {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\		& {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\
	& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256		& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256
	\end{align}</math>		\end{align}\,\!</math>

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

	::<math>\begin{align}		::<math>\begin{align}
	& \hat{\mu }= & 5.9281 \\		& \hat{\mu }= & 5.9281 \\
	& \hat{\sigma }= & 0.3821		& \hat{\sigma }= & 0.3821
	\end{align}</math>		\end{align}\,\!</math>

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

	::<math>\begin{align}		::<math>\begin{align}
	& \hat{\mu }= & 5.9772 \\		& \hat{\mu }= & 5.9772 \\
	& \hat{\sigma }= & 0.3256		& \hat{\sigma }= & 0.3256
	\end{align}</math>		\end{align}\,\!</math>

Chris Kahn: moved Example: Loglogistic Distribution to Loglogistic Distribution Example

2012-08-20T01:14:41Z

moved Example: Loglogistic Distribution to Loglogistic Distribution Example

← Older revision	Revision as of 01:14, 20 August 2012
(No difference)

Melinda Caroline at 07:05, 15 August 2012

2012-08-15T07:05:24Z

← Older revision		Revision as of 07:05, 15 August 2012
Line 28:		Line 28:
	\end{align}</math>		\end{align}</math>

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

	::<math>\begin{align}		::<math>\begin{align}
Line 35:		Line 35:
	\end{align}</math>		\end{align}</math>

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

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

Richard House at 07:49, 7 August 2012

2012-08-07T07:49:24Z

← Older revision		Revision as of 07:49, 7 August 2012
Line 19:		Line 19:
	\text{10} & \text{884} & \text{889} \\		\text{10} & \text{884} & \text{889} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	Set up the folio for times-to-failure data that includes interval and left censored data, then enter the data. The computed parameters for maximum likelihood are calculated to be:		Set up the folio for times-to-failure data that includes interval and left censored data, then enter the data. The computed parameters for maximum likelihood are calculated to be:
Line 26:		Line 27:
	& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256		& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256
	\end{align}</math>		\end{align}</math>


	For rank regression on <math>X\ \ :</math>		For rank regression on <math>X\ \ :</math>
Line 34:		Line 34:
	& \hat{\sigma }= & 0.3821		& \hat{\sigma }= & 0.3821
	\end{align}</math>		\end{align}</math>


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

Kate Racaza: proofread

2012-07-23T10:04:50Z

proofread

← Older revision		Revision as of 10:04, 23 July 2012
Line 1:		Line 1:
	{~~\| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"~~		<noinclude>{{Banner Weibull Examples}}
	\|-		''This example appears in the [[The_Loglogistic_Distribution#General_Examples\|Life Data Analysis Reference book]]''.</noinclude>
	~~\| valign="middle" align="left" bgcolor=EEEDF7\|~~[[~~Image:Weibull-Examples-banner.png~~\|~~400px\|center~~]]
	\|}
	<br>~~Determine the loglogistic parameter estimates for the data given in Table 10.3.~~

	<center><math>\overset{{}}{\mathop{\text{~~Table 10}\text{.3 -~~ Test data}}}\,</math></center>		Determine the loglogistic parameter estimates for the data given in the following table.

			<center><math>\overset{{}}{\mathop{\text{Test data}}}\,</math></center>

	<center><math>\begin{matrix}		<center><math>\begin{matrix}

Chris Kahn at 22:11, 3 May 2012

2012-05-03T22:11:48Z

← Older revision		Revision as of 22:11, 3 May 2012
Line 21:		Line 21:
	\end{matrix}</math></center>		\end{matrix}</math></center>

			Set up the folio for times-to-failure data that includes interval and left censored data, then enter the data. The computed parameters for maximum likelihood are calculated to be:
	~~Using Times~~-to-failure data ~~under the Folio Data Type and the My data set contains~~ interval and~~/or~~ left censored data ~~under Times-to-failure data options to~~ enter the ~~above~~ data~~, the~~ computed parameters for maximum likelihood are calculated to be:

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

Nicolette Young: Created page with '{| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;" |- | valign="middle" align="left" bgcolor=EEEDF7|[[Image:Weibull-E…'

2012-03-21T23:47:33Z

Created page with '{| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;" |- | valign="middle" align="left" bgcolor=EEEDF7|[[Image:Weibull-E…'

New page

{| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"
|-
| valign="middle" align="left" bgcolor=EEEDF7|[[Image:Weibull-Examples-banner.png|400px|center]]
|}
<br>Determine the loglogistic parameter estimates for the data given in Table 10.3.

<center><math>\overset{{}}{\mathop{\text{Table 10}\text{.3 - Test data}}}\,</math></center>

<center><math>\begin{matrix}
\text{Data point index} & \text{Last Inspected} & \text{State End time} \\
\text{1} & \text{105} & \text{106} \\
\text{2} & \text{197} & \text{200} \\
\text{3} & \text{297} & \text{301} \\
\text{4} & \text{330} & \text{335} \\
\text{5} & \text{393} & \text{401} \\
\text{6} & \text{423} & \text{426} \\
\text{7} & \text{460} & \text{468} \\
\text{8} & \text{569} & \text{570} \\
\text{9} & \text{675} & \text{680} \\
\text{10} & \text{884} & \text{889} \\
\end{matrix}</math></center>

Using Times-to-failure data under the Folio Data Type and the My data set contains interval and/or left censored data under Times-to-failure data options to enter the above data, the computed parameters for maximum likelihood are calculated to be:

::<math>\begin{align}
& {{{\hat{\mu }}}^{\prime }}= & 5.9772 \\
& {{{\hat{\sigma }}}_{{{T}'}}}= & 0.3256
\end{align}</math>

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

::<math>\begin{align}
& \hat{\mu }= & 5.9281 \\
& \hat{\sigma }= & 0.3821
\end{align}</math>

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

::<math>\begin{align}
& \hat{\mu }= & 5.9772 \\
& \hat{\sigma }= & 0.3256
\end{align}</math>