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- Timestamp:
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Mar 30, 2011, 3:49:21 PM (14 years ago)
- Author:
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Víctor de Buen Remiro
- Comment:
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v14
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v15
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74 | 74 | * the log-density function will be then [[BR]] [[BR]] |
75 | 75 | [[LatexEquation( \ln f\left(y;\mu,\sigma^{2}\right)= -\frac{1}{2}\ln\left(2\pi\sigma^{2}\right)-\frac{1}{2\sigma^{2}}\left(y}-\mu\right)^{2} )]][[BR]] [[BR]] |
76 | | * the partial derivative of log-density function respect to the linear prediction is [[BR]] [[BR]] |
| 76 | * the partial derivatives of log-density function respect to the linear prediction is [[BR]] [[BR]] |
77 | 77 | [[LatexEquation( \frac{\partial\ln f}{\partial\eta}=\frac{1}{\sigma^{2}}\left(y-\eta\right) )]] [[BR]] [[BR]] |
| 78 | [[LatexEquation( \frac{\partial^{2}\ln f}{\partial\eta^{2}}=-\frac{1}{\sigma^{2}} )]] [[BR]] [[BR]] |
78 | 79 | |
79 | 80 | === Weighted Poisson Regresion === |
… |
… |
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91 | 92 | * and its logarithm will be [[BR]] [[BR]] |
92 | 93 | [[LatexEquation( \ln f\left(y;\mu\right)=-\ln\left(y!\right)+y\ln\left(\mu\right)-\mu = -\ln\left(y!\right)+y\eta-e^{\eta} )]] |
93 | | * the partial derivative of log-density function respect to the linear prediction is [[BR]] [[BR]] |
| 94 | * the partial derivatives of log-density function respect to the linear prediction is [[BR]] [[BR]] |
94 | 95 | [[LatexEquation( \frac{\partial\ln f}{\partial\eta}=y-e^{\eta} )]] [[BR]] [[BR]] |
| 96 | [[LatexEquation( \frac{\partial^{2}\ln f}{\partial\eta^{2}}=-e^{\eta} )]] [[BR]] [[BR]] |
95 | 97 | |
96 | 98 | |