Template:Exponential Distribution Example: Likelihood Ratio Bound for Time - Revision history

Lisa Hacker: Redirected page to The Exponential Distribution

2012-08-10T08:42:25Z

Redirected page to The Exponential Distribution

← Older revision		Revision as of 08:42, 10 August 2012
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	~~'''Likelihood Ratio Bound on Time'''~~		#REDIRECT [[The Exponential Distribution]]

	~~For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%.~~ The ~~ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.~~

	~~'''Solution'''~~

	In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:

	~~::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>~~

Harry Guo at 18:28, 9 February 2012

2012-02-09T18:28:29Z

← Older revision		Revision as of 18:28, 9 February 2012
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	'''Likelihood Ratio Bound on Time'''		'''Likelihood Ratio Bound on Time'''

	For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.		For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.

Harry Guo: /* Example 6: Likelihood Ratio Bound on Time */

2012-02-09T18:28:12Z

Example 6: Likelihood Ratio Bound on Time

← Older revision		Revision as of 18:28, 9 February 2012
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	~~=====Example 6:~~ Likelihood Ratio Bound on Time~~=====~~		'''Likelihood Ratio Bound on Time'''
	For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.		For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.

	'''Solution ~~to Example 6~~'''		'''Solution'''

	In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:		In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:

	::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>		::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>

Harry Guo: /* Example 6: Likelihood Ratio Bound for Time */

2012-02-08T22:17:19Z

Example 6: Likelihood Ratio Bound for Time

← Older revision		Revision as of 22:17, 8 February 2012
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	=====Example 6: Likelihood Ratio Bound ~~for~~ Time=====		=====Example 6: Likelihood Ratio Bound on Time=====
	For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.		For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.

Harry Guo: /* Solution to Example 6 */

2012-02-08T22:15:09Z

Solution to Example 6

← Older revision		Revision as of 22:15, 8 February 2012
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	For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.		For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.

	~~======~~Solution to Example 6~~======~~		'''Solution to Example 6'''

	In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:		In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:

	::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>		::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>

Harry Guo: /* Example 6: Likelihood Ratio Bound for Time */

2012-02-08T22:11:33Z

Example 6: Likelihood Ratio Bound for Time

← Older revision		Revision as of 22:11, 8 February 2012
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	====Example 6: Likelihood Ratio Bound for Time====		=====Example 6: Likelihood Ratio Bound for Time=====
	For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.		For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.

	=====Solution to Example 6=====		======Solution to Example 6======
	In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:		In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:

	::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>		::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>

Harry Guo: moved Template:Exponential Distribution: Likelihood Ratio Bound for Time to Template:Exponential Distribution Example: Likelihood Ratio Bound for Time

2012-02-08T00:39:20Z

moved Template:Exponential Distribution: Likelihood Ratio Bound for Time to Template:Exponential Distribution Example: Likelihood Ratio Bound for Time

← Older revision	Revision as of 00:39, 8 February 2012
(No difference)

Harry Guo: /* Example 6: Likelihood Ratio Bound for Time */

2012-02-08T00:38:17Z

Example 6: Likelihood Ratio Bound for Time

← Older revision		Revision as of 00:38, 8 February 2012
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	====Example 6: Likelihood Ratio Bound for Time====		====Example 6: Likelihood Ratio Bound for Time====
	For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797</math>.		For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797.</math>.

	=====Solution to Example 6=====		=====Solution to Example 6=====

Harry Guo: Created page with '====Example 6: Likelihood Ratio Bound for Time==== For the data given in Example 5: Likelihood Ratio Bound for $\lambda$ , determine the 85% two-sided confidence bound…'

2012-02-08T00:32:41Z

Created page with '====Example 6: Likelihood Ratio Bound for Time==== For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bound…'

New page

====Example 6: Likelihood Ratio Bound for Time====
For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797</math>.

=====Solution to Example 6=====
In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:

::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>

Template:Exponential Distribution Example: Likelihood Ratio Bound for Time - Revision history

Lisa Hacker: Redirected page to The Exponential Distribution

Harry Guo at 18:28, 9 February 2012

Harry Guo: /* Example 6: Likelihood Ratio Bound on Time */

Harry Guo: /* Example 6: Likelihood Ratio Bound for Time */

Harry Guo: /* Solution to Example 6 */

Harry Guo: /* Example 6: Likelihood Ratio Bound for Time */

Harry Guo: moved Template:Exponential Distribution: Likelihood Ratio Bound for Time to Template:Exponential Distribution Example: Likelihood Ratio Bound for Time

Harry Guo: /* Example 6: Likelihood Ratio Bound for Time */

Harry Guo: Created page with '====Example 6: Likelihood Ratio Bound for Time==== For the data given in Example 5: Likelihood Ratio Bound for \lambda , determine the 85% two-sided confidence bound…'

Harry Guo: Created page with '====Example 6: Likelihood Ratio Bound for Time==== For the data given in Example 5: Likelihood Ratio Bound for $\lambda$ , determine the 85% two-sided confidence bound…'