Template:Eyring-ex mle - Revision history

Richard House: Redirected page to Eyring Relationship#Eyring-Exponential

2012-08-16T23:08:43Z

Redirected page to Eyring Relationship#Eyring-Exponential

← Older revision		Revision as of 23:08, 16 August 2012
Line 1:		Line 1:
	~~====Maximum Likelihood Estimation Method====~~		#REDIRECT [[Eyring_Relationship#Eyring-Exponential]]
	~~<br>~~

	~~The complete exponential log-likelihood function of the Eyring model is composed of two summation portions:~~

	~~<br>~~
	~~::<math>\begin{align}~~
	~~& \ln (L)= & \Lambda =\underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\ln \left~~[ {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{e}^{-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot {{T}_{i}}}} \right] -\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot T_{i}^{\prime }+\overset{FI}{\mathop{\underset{i=1}{\mathop{\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\ln [~~R_{Li}^{\prime \prime }~~-~~R_{Ri}^{\prime \prime }~~]
	~~\end{align}</math>~~

	~~<br>~~
	~~:where:~~

	~~<br>~~
	~~::<math>R_{Li}^{\prime \prime }={{e}^{-T_{Li}^{\prime \prime }{{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}}</math>~~

	~~<br>~~
	~~::<math>R_{Ri}^{\prime \prime }={{e}^{-T_{Ri}^{\prime \prime }{{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}}</math>~~

	~~<br>~~
	~~and:~~

	~~• <math>{{F}_{e}}</math> is the number of groups of exact times-to-failure data points.~~
	~~<br>~~
	~~• <math>{{N}_{i}}</math> is the number of times-to-failure in the <math>{{i}^{th}}</math> time-to-failure data group.~~
	~~<br>~~
	~~• <math>{{V}_{i}}</math> is the stress level of the <math>{{i}^{th}}</math> group.~~
	~~<br>~~
	~~• <math>A</math> is the Eyring parameter (unknown, the first of two parameters to be estimated).~~
	~~<br>~~
	~~• <math>B</math> is the second Eyring parameter (unknown, the second of two parameters to be estimated).~~
	~~<br>~~
	~~• <math>{{T}_{i}}</math> is the exact failure time of the <math>{{i}^{th}}</math> group.~~
	~~<br>~~
	~~• <math>S</math> is the number of groups of suspension data points.~~
	~~<br>~~
	~~• <math>N_{i}^{\prime }</math> is the number of suspensions in the <math>{{i}^{th}}</math> group of suspension data points.~~
	~~<br>~~
	~~• <math>T_{i}^{\prime }</math> is the running time of the <math>{{i}^{th}}</math> suspension data group.~~
	~~<br>~~
	~~• <math>FI</math> is the number of interval data groups.~~
	~~<br>~~
	~~• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the <math>{{i}^{th}}</math> group of data intervals.~~
	~~<br>~~
	~~• <math>T_{Li}^{\prime \prime }</math> is the beginning of the <math>{{i}^{th}}</math> interval.~~
	~~<br>~~
	~~• <math>T_{Ri}^{\prime \prime }</math> is the ending of the <math>{{i}^{th}}</math> interval.~~
	~~<br>~~
	The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:


	~~<br>~~
	~~::<math>\begin{align}~~
	& \frac{\partial \Lambda }{\partial A}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left( 1-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}} \right)-\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \overset{FI}{\mathop{\underset{i=1}{\mathop{-\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
	~~\end{align}</math>~~

	~~<br>~~
	~~::<math>\begin{align}~~
	~~& \frac{\partial \Lambda }{\partial B}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left[ {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}}-\frac{1}{{{V}_{i}}} \right~~]+\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \overset{FI}{\mathop{\underset{i=1}{\mathop{+\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
	~~\end{align}</math>~~

	~~<br>~~

Chris Kahn: /* Maximum Likelihood Estimation Method */

2012-03-09T17:57:58Z

Maximum Likelihood Estimation Method

← Older revision		Revision as of 17:57, 9 March 2012
Line 41:		Line 41:
	• <math>FI</math> is the number of interval data groups.		• <math>FI</math> is the number of interval data groups.
	<br>		<br>
	• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the i <math>^{th}</math> group of data intervals.		• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the <math>{{i}^{th}}</math> group of data intervals.
	<br>		<br>
	• <math>T_{Li}^{\prime \prime }</math> is the beginning of the i <math>^{th}</math> interval.		• <math>T_{Li}^{\prime \prime }</math> is the beginning of the <math>{{i}^{th}}</math> interval.
	<br>		<br>
	• <math>T_{Ri}^{\prime \prime }</math> is the ending of the i <math>^{th}</math> interval.		• <math>T_{Ri}^{\prime \prime }</math> is the ending of the <math>{{i}^{th}}</math> interval.
	<br>		<br>
	The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:		The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:

Chris Kahn: Undo revision 20745 by Chris Kahn (Talk)

2012-03-09T17:57:24Z

Undo revision 20745 by Chris Kahn (Talk)

← Older revision		Revision as of 17:57, 9 March 2012
Line 41:		Line 41:
	• <math>FI</math> is the number of interval data groups.		• <math>FI</math> is the number of interval data groups.
	<br>		<br>
	• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the <math>{~~{T}_{i}~~}</math> group of data intervals.		• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the i <math>^{th}</math> group of data intervals.
	<br>		<br>
	• <math>T_{Li}^{\prime \prime }</math> is the beginning of the <math>{~~{T}_{i}~~}</math> interval.		• <math>T_{Li}^{\prime \prime }</math> is the beginning of the i <math>^{th}</math> interval.
	<br>		<br>
	• <math>T_{Ri}^{\prime \prime }</math> is the ending of the <math>{~~{T}_{i}~~}</math> interval.		• <math>T_{Ri}^{\prime \prime }</math> is the ending of the i <math>^{th}</math> interval.
	<br>		<br>
	The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:		The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:

Chris Kahn: /* Maximum Likelihood Estimation Method */

2012-03-09T17:56:23Z

Maximum Likelihood Estimation Method

← Older revision		Revision as of 17:56, 9 March 2012
Line 41:		Line 41:
	• <math>FI</math> is the number of interval data groups.		• <math>FI</math> is the number of interval data groups.
	<br>		<br>
	• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the i <math>^{th}</math> group of data intervals.		• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the <math>{{T}_{i}}</math> group of data intervals.
	<br>		<br>
	• <math>T_{Li}^{\prime \prime }</math> is the beginning of the i <math>^{th}</math> interval.		• <math>T_{Li}^{\prime \prime }</math> is the beginning of the <math>{{T}_{i}}</math> interval.
	<br>		<br>
	• <math>T_{Ri}^{\prime \prime }</math> is the ending of the i <math>^{th}</math> interval.		• <math>T_{Ri}^{\prime \prime }</math> is the ending of the <math>{{T}_{i}}</math> interval.
	<br>		<br>
	The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:		The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:

Athanasios Gerokostopoulos: /* Maximum Likelihood Estimation Method */

2012-02-14T22:45:04Z

Maximum Likelihood Estimation Method

← Older revision		Revision as of 22:45, 14 February 2012
Line 19:		Line 19:

	<br>		<br>
	:and:		and:
	~~<br>~~
	• <math>{{F}_{e}}</math> is the number of groups of exact times-to-failure data points.		• <math>{{F}_{e}}</math> is the number of groups of exact times-to-failure data points.
	<br>		<br>

Athanasios Gerokostopoulos: /* Maximum Likelihood Estimation Method */

2012-02-14T22:44:30Z

Maximum Likelihood Estimation Method

← Older revision		Revision as of 22:44, 14 February 2012
Line 6:		Line 6:
	<br>		<br>
	::<math>\begin{align}		::<math>\begin{align}
	& \ln (L)= & \Lambda =\underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\ln \left[ {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{e}^{-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot {{T}_{i}}}} \right] \\		& \ln (L)= & \Lambda =\underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\ln \left[ {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{e}^{-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot {{T}_{i}}}} \right] -\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot T_{i}^{\prime }+\overset{FI}{\mathop{\underset{i=1}{\mathop{\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\ln [R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }]
	~~& &~~ -\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot T_{i}^{\prime }+\overset{FI}{\mathop{\underset{i=1}{\mathop{\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\ln [R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }]
	\end{align}</math>		\end{align}</math>

Line 53:		Line 52:
	<br>		<br>
	::<math>\begin{align}		::<math>\begin{align}
	& \frac{\partial \Lambda }{\partial A}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left( 1-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}} \right)-\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \\		& \frac{\partial \Lambda }{\partial A}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left( 1-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}} \right)-\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \overset{FI}{\mathop{\underset{i=1}{\mathop{-\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
	~~& &~~ \overset{FI}{\mathop{\underset{i=1}{\mathop{-\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
	\end{align}</math>		\end{align}</math>

	<br>		<br>
	::<math>\begin{align}		::<math>\begin{align}
	& \frac{\partial \Lambda }{\partial B}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left[ {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}}-\frac{1}{{{V}_{i}}} \right]+\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \\		& \frac{\partial \Lambda }{\partial B}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left[ {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}}-\frac{1}{{{V}_{i}}} \right]+\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \overset{FI}{\mathop{\underset{i=1}{\mathop{+\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
	~~& &~~ \overset{FI}{\mathop{\underset{i=1}{\mathop{+\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
	\end{align}</math>		\end{align}</math>

	<br>		<br>

Nicolette Young: Created page with '====Maximum Likelihood Estimation Method====
The complete exponential log-likelihood function of the Eyring model is composed of two summation portions:
:: $\begi…'$

2012-01-12T22:39:13Z

Created page with '====Maximum Likelihood Estimation Method==== The complete exponential log-likelihood function of the Eyring model is composed of two summation portions: ::<math>\begi…'

New page

====Maximum Likelihood Estimation Method====
 

The complete exponential log-likelihood function of the Eyring model is composed of two summation portions:

 
::<math>\begin{align}
& \ln (L)= & \Lambda =\underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\ln \left[ {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{e}^{-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot {{T}_{i}}}} \right] \\
& & -\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}\cdot T_{i}^{\prime }+\overset{FI}{\mathop{\underset{i=1}{\mathop{\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\ln [R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }]
\end{align}</math>

 
:where:

 
::<math>R_{Li}^{\prime \prime }={{e}^{-T_{Li}^{\prime \prime }{{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}}</math>

 
::<math>R_{Ri}^{\prime \prime }={{e}^{-T_{Ri}^{\prime \prime }{{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}}</math>

 
:and:
 
• <math>{{F}_{e}}</math> is the number of groups of exact times-to-failure data points.
 
• <math>{{N}_{i}}</math> is the number of times-to-failure in the <math>{{i}^{th}}</math> time-to-failure data group.
 
• <math>{{V}_{i}}</math> is the stress level of the <math>{{i}^{th}}</math> group.
 
• <math>A</math> is the Eyring parameter (unknown, the first of two parameters to be estimated).
 
• <math>B</math> is the second Eyring parameter (unknown, the second of two parameters to be estimated).
 
• <math>{{T}_{i}}</math> is the exact failure time of the <math>{{i}^{th}}</math> group.
 
• <math>S</math> is the number of groups of suspension data points.
 
• <math>N_{i}^{\prime }</math> is the number of suspensions in the <math>{{i}^{th}}</math> group of suspension data points.
 
• <math>T_{i}^{\prime }</math> is the running time of the <math>{{i}^{th}}</math> suspension data group.
 
• <math>FI</math> is the number of interval data groups.
 
• <math>N_{i}^{\prime \prime }</math> is the number of intervals in the i <math>^{th}</math> group of data intervals.
 
• <math>T_{Li}^{\prime \prime }</math> is the beginning of the i <math>^{th}</math> interval.
 
• <math>T_{Ri}^{\prime \prime }</math> is the ending of the i <math>^{th}</math> interval.
 
The solution (parameter estimates) will be found by solving for the parameters <math>\widehat{A}</math> and <math>\widehat{B}</math> so that <math>\tfrac{\partial \Lambda }{\partial A}=0</math> and <math>\tfrac{\partial \Lambda }{\partial B}=0</math> where:

 
::<math>\begin{align}
& \frac{\partial \Lambda }{\partial A}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left( 1-{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}} \right)-\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }{{V}_{i}}\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \\
& & \overset{FI}{\mathop{\underset{i=1}{\mathop{-\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{V}_{i}}{{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
\end{align}</math>

 
::<math>\begin{align}
& \frac{\partial \Lambda }{\partial B}= & \underset{i=1}{\overset{{{F}_{e}}}{\mathop \sum }}\,{{N}_{i}}\left[ {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}{{T}_{i}}-\frac{1}{{{V}_{i}}} \right]+\underset{i=1}{\overset{S}{\mathop \sum }}\,N_{i}^{\prime }\cdot {{e}^{\left( A-\tfrac{B}{{{V}_{i}}} \right)}}T_{i}^{\prime } \\
& & \overset{FI}{\mathop{\underset{i=1}{\mathop{+\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,N_{i}^{\prime \prime }\frac{\left( T_{Li}^{\prime \prime }R_{Li}^{\prime \prime }-T_{Ri}^{\prime \prime }R_{Ri}^{\prime \prime } \right){{e}^{A-\tfrac{B}{{{V}_{i}}}}}}{R_{Li}^{\prime \prime }-R_{Ri}^{\prime \prime }}
\end{align}</math>

Template:Eyring-ex mle - Revision history

Richard House: Redirected page to Eyring Relationship#Eyring-Exponential

Chris Kahn: /* Maximum Likelihood Estimation Method */

Chris Kahn: Undo revision 20745 by Chris Kahn (Talk)

Chris Kahn: /* Maximum Likelihood Estimation Method */

Athanasios Gerokostopoulos: /* Maximum Likelihood Estimation Method */

Athanasios Gerokostopoulos: /* Maximum Likelihood Estimation Method */

Nicolette Young: Created page with '====Maximum Likelihood Estimation Method==== The complete exponential log-likelihood function of the Eyring model is composed of two summation portions: ::\begi…'

Nicolette Young: Created page with '====Maximum Likelihood Estimation Method====
The complete exponential log-likelihood function of the Eyring model is composed of two summation portions:
:: $\begi…'$