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Difference between revisions of "User:Ulf Rehmann/sandbox statprob/"

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(Created page with "\begin{table} <!-- \noindent --> '''Table 1.''' A class of stationary correlation models for longitudinal count data and basic properties. <center> \begin{array}{ccc} Model &...")
 
 
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\begin{table}
+
This code  produces some nested array image.
<!-- \noindent -->
+
 
 
'''Table 1.''' A class of stationary correlation models for longitudinal count data
 
'''Table 1.''' A class of stationary correlation models for longitudinal count data
 
and basic properties.
 
and basic properties.
 
<center>
 
<center>
\begin{array}{ccc}
+
$$\begin{array}{ccc}
Model & Dynamic relationship & Mean-variance \\
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\text{Model} & \text{Dynamic relationship} & \text{Mean-variance} \\
&& \& Correlations \\ \hline
+
&& \text{\& Correlations} \\ \hline
 
AR(1) &  y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots  &  E[Y_{it}]=\mu_{i\cdot}  \\
 
AR(1) &  y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots  &  E[Y_{it}]=\mu_{i\cdot}  \\
 
&  y_{i1}\sim Poi(\mu_{i\cdot})  &  \mbox{var}[Y_{it}]=\mu_{i\cdot}  \\
 
&  y_{i1}\sim Poi(\mu_{i\cdot})  &  \mbox{var}[Y_{it}]=\mu_{i\cdot}  \\
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&  y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho))  &  \mbox{var}[Y_{it}]=\mu_{i\cdot}  \\
 
&  y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho))  &  \mbox{var}[Y_{it}]=\mu_{i\cdot}  \\
 
&  d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots &  \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell}  \\
 
&  d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots &  \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell}  \\
&& $=
+
&& =
 
\left\{ \begin{array}{ll}
 
\left\{ \begin{array}{ll}
 
\frac{\rho}{1+\rho} & \mbox{for } \ell=1\\
 
\frac{\rho}{1+\rho} & \mbox{for } \ell=1\\
 
0 & \mbox{otherwise},
 
0 & \mbox{otherwise},
\end{array} \right.$
+
\end{array} \right.
 
\\ \hline
 
\\ \hline
 
EQC &  y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots  &  E[Y_{it}]=\mu_{i\cdot}  \\
 
EQC &  y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots  &  E[Y_{it}]=\mu_{i\cdot}  \\
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&  d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots &  \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell}  \\
 
&  d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots &  \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell}  \\
 
&&  =\rho  \\ \hline
 
&&  =\rho  \\ \hline
\end{array}
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\end{array}$$
 
</center>
 
</center>
\end{table}
 

Latest revision as of 11:12, 12 March 2015

This code produces some nested array image.

Table 1. A class of stationary correlation models for longitudinal count data and basic properties.

$$\begin{array}{ccc} \text{Model} & \text{Dynamic relationship} & \text{Mean-variance} \\ && \text{\& Correlations} \\ \hline AR(1) & y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && =\rho^{\ell} \\ \hline MA(1) & y_{it}=\rho * d_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho)) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && = \left\{ \begin{array}{ll} \frac{\rho}{1+\rho} & \mbox{for } \ell=1\\ 0 & \mbox{otherwise}, \end{array} \right. \\ \hline EQC & y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && =\rho \\ \hline \end{array}$$

How to Cite This Entry:
Ulf Rehmann/sandbox statprob/. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ulf_Rehmann/sandbox_statprob/&oldid=36325