Changes between Version 11 and Version 12 of OfficialTolArchiveNetworkGrzLinModel

Timestamp:

Mar 30, 2011, 2:58:25 PM (15 years ago)

Author:

Víctor de Buen Remiro

Comment:

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OfficialTolArchiveNetworkGrzLinModel

@@ -60 +60 @@
  * the identity as link function and mean function [[BR]] [[BR]] 
    [[LatexEquation( \eta = g\left(\mu\right)= \mu = g^{-1}\left(\eta\right) = \eta)]] [[BR]] [[BR]] 
- * the log-density function has the variance as extra parameter[[BR]] [[BR]] 
+ * the density function has the variance as extra parameter[[BR]] [[BR]] 
+   [[LatexEquation( f\left(y;\mu,\sigma^{2}\right)=\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{^{-\frac{1}{2}\frac{\left(y-\mu\right)^{2}}{\sigma^{2}}}} )]][[BR]] [[BR]] 
+ * the log-density function will be then [[BR]] [[BR]] 
    [[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} )]]
 
@@ -74 +76 @@
  * the mean function [[BR]] [[BR]] 
    [[LatexEquation( \mu = g^{-1}\left(\eta\right)=\exp\left(\eta\right) )]] [[BR]]  [[BR]]
- * the log-probability mass function [[BR]] [[BR]] 
-   [[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})]]
+ * the probability mass function [[BR]] [[BR]] 
+   [[LatexEquation( f\left(y;\mu\right)=\frac{1}{y!}e^{-\mu}\mu^{y} )]]
+ * and its logarithm will be [[BR]] [[BR]] 
+   [[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} )]]