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# Discrete Distributions
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Discrete probability distributions for modeling categorical and binary outcomes, including various parameterizations for different use cases.
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## Capabilities
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### Bernoulli Distribution
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Binary distribution for modeling binary outcomes.
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```python { .api }
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class Bernoulli(Distribution):
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    def __init__(self, logits=None, probs=None, dtype=int):
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        """
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        Bernoulli distribution for binary outcomes.
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        Parameters:
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        - logits: log-odds parameter (float or array, mutually exclusive with probs)
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        - probs: probability parameter (float or array in [0,1], mutually exclusive with logits)
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        - dtype: output data type (int or float)
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        Note: Exactly one of logits or probs must be specified.
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        """
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    @property
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    def logits(self): ...
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    @property
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    def probs(self): ...
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    @property
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    def dtype(self): ...
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    @property
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    def event_shape(self): ...
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```
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### Categorical Distribution
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Categorical distribution for discrete outcomes with multiple categories.
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```python { .api }
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class Categorical(Distribution):
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    def __init__(self, logits=None, probs=None, dtype=int):
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        """
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        Categorical distribution for discrete outcomes.
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        Parameters:
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        - logits: log-probabilities (array of shape [..., k], mutually exclusive with probs)
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        - probs: probabilities (array of shape [..., k] that sums to 1, mutually exclusive with logits)
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        - dtype: output data type (int or float)
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        Note: Exactly one of logits or probs must be specified.
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        """
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    @property
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    def logits(self): ...
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    @property
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    def probs(self): ...
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    @property
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    def dtype(self): ...
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    @property
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    def num_categories(self): ...
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    @property
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    def event_shape(self): ...
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```
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### One-Hot Categorical Distribution
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Categorical distribution with one-hot encoded outcomes.
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```python { .api }
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class OneHotCategorical(Distribution):
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    def __init__(self, logits=None, probs=None, dtype=float):
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        """
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        One-hot categorical distribution.
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        Parameters:
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        - logits: log-probabilities (array of shape [..., k], mutually exclusive with probs)
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        - probs: probabilities (array of shape [..., k] that sums to 1, mutually exclusive with logits)
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        - dtype: output data type (float or int)
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        Note: Exactly one of logits or probs must be specified.
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        """
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    @property
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    def logits(self): ...
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    @property
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    def probs(self): ...
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    @property
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    def dtype(self): ...
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    @property
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    def num_categories(self): ...
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    @property
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    def event_shape(self): ...
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```
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### Categorical Uniform Distribution
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Uniform categorical distribution over all categories.
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```python { .api }
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class CategoricalUniform(Distribution):
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    def __init__(self, num_categories, dtype=int):
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        """
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        Uniform categorical distribution.
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        Parameters:
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        - num_categories: number of categories (positive integer)
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        - dtype: output data type (int or float)
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        """
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    @property
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    def num_categories(self): ...
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    @property
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    def dtype(self): ...
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    @property
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    def logits(self): ...
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    @property
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    def probs(self): ...
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```
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### Multinomial Distribution
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Multinomial distribution for modeling counts across multiple categories.
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```python { .api }
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class Multinomial(Distribution):
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    def __init__(self, total_count, logits=None, probs=None, dtype=int):
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        """
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        Multinomial distribution.
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        Parameters:
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        - total_count: total number of trials (positive integer or array)
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        - logits: log-probabilities for each category (array, mutually exclusive with probs)
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        - probs: probabilities for each category (array that sums to 1, mutually exclusive with logits)
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        - dtype: output data type (int or float)
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        Note: Exactly one of logits or probs must be specified.
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        """
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    @property
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    def total_count(self): ...
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    @property
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    def logits(self): ...
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    @property
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    def probs(self): ...
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    @property
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    def event_shape(self): ...
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```
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### Softmax Distribution
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Softmax distribution for normalized discrete outcomes.
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```python { .api }
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class Softmax(Distribution):
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    def __init__(self, logits, temperature=1.0):
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        """
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        Softmax distribution.
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        Parameters:
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        - logits: unnormalized log-probabilities (array of shape [..., k])
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        - temperature: temperature parameter for softmax (positive float, default 1.0)
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        """
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    @property
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    def logits(self): ...
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    @property
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    def temperature(self): ...
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    @property
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    def probs(self): ...
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```