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

Chris Kahn: Redirected page to The Lognormal Distribution

2012-08-14T07:56:01Z

Redirected page to The Lognormal Distribution

← Older revision		Revision as of 07:56, 14 August 2012
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	~~'''~~Lognormal Distribution ~~General Example Complete Data Unbiased MLE'''~~		#REDIRECT [[The Lognormal Distribution]]

	~~From [[Appendix: Weibull References\|Kececioglu [19, p. 406]~~]]~~. Nine identical units are tested continuously to failure and their times-to-failure were recorded at 30.4, 36.7, 53.3, 58.5, 74.0, 99.3, 114.3, 140.1, and 257.9 hours.~~

	~~'''Solution'''~~

	~~The results published were obtained by using the unbiased model.~~
	~~Published Results (using MLE):~~

	~~::<math>\begin{matrix}~~
	~~{{\widehat{\mu }}^{\prime }}=4.3553 \\~~
	~~{{\widehat{\sigma' }}}=0.67677 \\~~
	~~\end{matrix}</math>~~

	This same data set can be entered into Weibull++ by creating a data sheet capable of handling non-grouped time-to-failure data. Since the results shown above are unbiased, the Use Unbiased Std on Normal Data option in the User Setup must be selected in order to duplicate these results.
	~~Weibull++ computed parameters for maximum likelihood are:~~

	~~::<math>\begin{matrix}~~
	~~{{\widehat{\mu }}^{\prime }}=4.3553 \\~~
	~~{{\widehat{\sigma' }}}=0.6768 \\~~
	~~\end{matrix}</math>~~

Richard House at 05:06, 8 August 2012

2012-08-08T05:06:59Z

← Older revision		Revision as of 05:06, 8 August 2012
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	{{\widehat{\sigma' }}}=0.67677 \\		{{\widehat{\sigma' }}}=0.67677 \\
	\end{matrix}</math>		\end{matrix}</math>


	This same data set can be entered into Weibull++ by creating a data sheet capable of handling non-grouped time-to-failure data. Since the results shown above are unbiased, the Use Unbiased Std on Normal Data option in the User Setup must be selected in order to duplicate these results.		This same data set can be entered into Weibull++ by creating a data sheet capable of handling non-grouped time-to-failure data. Since the results shown above are unbiased, the Use Unbiased Std on Normal Data option in the User Setup must be selected in order to duplicate these results.
	Weibull++ computed parameters for maximum likelihood are:		Weibull++ computed parameters for maximum likelihood are:


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

Harry Guo at 23:46, 13 February 2012

2012-02-13T23:46:59Z

← Older revision		Revision as of 23:46, 13 February 2012
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	'''Lognormal Distribution General Example Complete Data Unbiased MLE'''		'''Lognormal Distribution General Example Complete Data Unbiased MLE'''

	From Kececioglu [19, p. 406]. Nine identical units are tested continuously to failure and their times-to-failure were recorded at 30.4, 36.7, 53.3, 58.5, 74.0, 99.3, 114.3, 140.1, and 257.9 hours.		From [[Appendix: Weibull References\|Kececioglu [19, p. 406]]]. Nine identical units are tested continuously to failure and their times-to-failure were recorded at 30.4, 36.7, 53.3, 58.5, 74.0, 99.3, 114.3, 140.1, and 257.9 hours.

	'''Solution'''		'''Solution'''
Line 10:		Line 10:
	::<math>\begin{matrix}		::<math>\begin{matrix}
	{{\widehat{\mu }}^{\prime }}=4.3553 \\		{{\widehat{\mu }}^{\prime }}=4.3553 \\
	{{\widehat{\sigma ~~}}_{{{T}~~'}}}=0.67677 \\		{{\widehat{\sigma' }}}=0.67677 \\
	\end{matrix}</math>		\end{matrix}</math>

Line 20:		Line 20:
	::<math>\begin{matrix}		::<math>\begin{matrix}
	{{\widehat{\mu }}^{\prime }}=4.3553 \\		{{\widehat{\mu }}^{\prime }}=4.3553 \\
	{{\widehat{\sigma ~~}}_{{{T}~~'}}}=0.6768 \\		{{\widehat{\sigma' }}}=0.6768 \\
	\end{matrix}</math>		\end{matrix}</math>

Harry Guo: Created page with ''''Lognormal Distribution General Example Complete Data Unbiased MLE''' From Kececioglu [19, p. 406]. Nine identical units are tested continuously to failure and their times-to-…'

2012-02-13T19:01:16Z

Created page with ''''Lognormal Distribution General Example Complete Data Unbiased MLE''' From Kececioglu [19, p. 406]. Nine identical units are tested continuously to failure and their times-to-…'

New page

'''Lognormal Distribution General Example Complete Data Unbiased MLE'''

From Kececioglu [19, p. 406]. Nine identical units are tested continuously to failure and their times-to-failure were recorded at 30.4, 36.7, 53.3, 58.5, 74.0, 99.3, 114.3, 140.1, and 257.9 hours.

'''Solution'''

The results published were obtained by using the unbiased model.
Published Results (using MLE):

::<math>\begin{matrix}
{{\widehat{\mu }}^{\prime }}=4.3553 \\
{{\widehat{\sigma }}_{{{T}'}}}=0.67677 \\
\end{matrix}</math>

This same data set can be entered into Weibull++ by creating a data sheet capable of handling non-grouped time-to-failure data. Since the results shown above are unbiased, the Use Unbiased Std on Normal Data option in the User Setup must be selected in order to duplicate these results.
Weibull++ computed parameters for maximum likelihood are:

::<math>\begin{matrix}
{{\widehat{\mu }}^{\prime }}=4.3553 \\
{{\widehat{\sigma }}_{{{T}'}}}=0.6768 \\
\end{matrix}</math>