Template:Gll weibull: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
|||
| Line 1: | Line 1: | ||
====GLL Weibull==== | ====GLL Weibull==== | ||
The GLL-Weibull model can be derived by setting <math>\eta =L(\underline{X})</math> in | The GLL-Weibull model can be derived by setting <math>\eta =L(\underline{X})</math> in Weibull <math>pdf</math>, yielding the following GLL-Weibull <math>pdf</math> : | ||
<br> | <br> | ||
<math>f(t,\underline{X})=\beta \cdot {{t}^{\beta -1}}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}{{e}^{-{{t}^{\beta }}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}}}</math> | <math>f(t,\underline{X})=\beta \cdot {{t}^{\beta -1}}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}{{e}^{-{{t}^{\beta }}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}}}</math> | ||
<br> | <br> | ||
The total number of unknowns to solve for in this model is <math>n+2</math> (i.e. <math>\beta ,{{a}_{0}},{{a}_{1}},...{{a}_{n}}).</math> | The total number of unknowns to solve for in this model is <math>n+2</math> (i.e. <math>\beta ,{{a}_{0}},{{a}_{1}},...{{a}_{n}}).</math> | ||
<br> | <br> | ||
Revision as of 22:02, 20 February 2012
GLL Weibull
The GLL-Weibull model can be derived by setting [math]\displaystyle{ \eta =L(\underline{X}) }[/math] in Weibull [math]\displaystyle{ pdf }[/math], yielding the following GLL-Weibull [math]\displaystyle{ pdf }[/math] :
[math]\displaystyle{ f(t,\underline{X})=\beta \cdot {{t}^{\beta -1}}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}{{e}^{-{{t}^{\beta }}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}}} }[/math]
The total number of unknowns to solve for in this model is [math]\displaystyle{ n+2 }[/math] (i.e. [math]\displaystyle{ \beta ,{{a}_{0}},{{a}_{1}},...{{a}_{n}}). }[/math]