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troubleshoot math
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jykr committed Jun 21, 2024
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6 changes: 3 additions & 3 deletions docs/model.rst
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Expand Up @@ -447,9 +447,9 @@ values using method-of-moments. For
.. math::
V^{(k)} = Var\left( X^{(k)} \right) = np^{(k)}\ \left( 1 - p^{(k)} \right)\left( 1 + \frac{n - 1}{1 + \alpha^{\circ}} \right)\
V^{(k)} = Var \left( X^{(k)} \right) = np^{(k)} \left( 1 - p^{(k)} \right) \left( 1 + \frac{n - 1}{1 + \alpha^{\circ}} \right)
Where
:math:`p^{(k)} = \frac{\alpha^{\left( k \right)}}{\alpha^{\circ}}`.
Expand All @@ -466,7 +466,7 @@ Given :math:`n`, we can get the method-of-moment estimates of
.. math::
\widehat{\alpha^{\circ}} = \left( \sum_{k \in \left\{ 1\ldots d \right\}}^{}{\frac{n - 1}{\frac{\widehat{V^{(k)}} - \widehat{\mu^{(k)}}}{n\widehat{p^{(k)}}\left( 1 - \widehat{p^{(k)}} \right)} - 1 + \frac{1}{1 - \widehat{p^{(k)}}}} - 1} \right)/d\
\widehat{\alpha^{\circ}} = \left( \sum_{k \in \{ 1 \ldots d \}}^{}{\frac{n - 1}{\frac{\widehat{V^{(k)}} - \widehat{\mu^{(k)}}}{n\widehat{p^{(k)}} \left( 1 - \widehat{p^{(k)}} \right) } - 1 + \frac{1}{1 - \widehat{p^{(k)}}}} - 1} \right)/d
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