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→Link function: Table - Corrected swapped Binomial and Bernoulli distribution names Tags: Reverted Visual edit |
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| integer: <math>0,1,2,\ldots</math> || count of occurrences in fixed amount of time/space || [[Natural logarithm|Log]] || <math>\mathbf{X}\boldsymbol{\beta} = \ln(\mu) \,\!</math> || <math>\mu=\exp (\mathbf{X}\boldsymbol{\beta}) \,\!</math>
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| integer: <math>\{0,1\}</math> || outcome of single yes/no occurrence
| rowspan="5" | [[Logit]]
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| rowspan="5" | <math>\mu=\frac{\exp(\mathbf{X}\boldsymbol{\beta})}{1 + \exp(\mathbf{X}\boldsymbol{\beta})} = \frac 1 {1 + \exp(-\mathbf{X} \boldsymbol{\beta})} \,\!</math>
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| integer: <math>0,1,\ldots,N</math> || count of # of "yes" occurrences out of N yes/no occurrences
|<math>\mathbf{X}\boldsymbol{\beta}=\ln \left(\frac \mu {n-\mu}\right) \,\!</math>
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For categorical and multinomial distributions, the parameter to be predicted is a ''K''-vector of probabilities, with the further restriction that all probabilities must add up to 1. Each probability indicates the likelihood of occurrence of one of the ''K'' possible values. For the multinomial distribution, and for the vector form of the categorical distribution, the expected values of the elements of the vector can be related to the predicted probabilities similarly to the binomial and Bernoulli distributions.
== Fitting ==
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