Beta distribution.

This distribution is parameterized by `a` and `b` which are shape
parameters.

#### Mathematical details

The Beta is a distribution over the interval (0, 1).
The distribution has hyperparameters `a` and `b` and
probability mass function (pdf):

```pdf(x) = 1 / Beta(a, b) * x^(a - 1) * (1 - x)^(b - 1)```

where `Beta(a, b) = Gamma(a) * Gamma(b) / Gamma(a + b)`
is the beta function.


This class provides methods to create indexed batches of Beta
distributions. One entry of the broadcasted
shape represents of `a` and `b` represents one single Beta distribution.
When calling distribution functions (e.g. `dist.pdf(x)`), `a`, `b`
and `x` are broadcast to the same shape (if possible).
Every entry in a/b/x corresponds to a single Beta distribution.

#### Examples

Creates 3 distributions.
The distribution functions can be evaluated on x.

```python
a = [1, 2, 3]
b = [1, 2, 3]
dist = Beta(a, b)
```

```python
# x same shape as a.
x = [.2, .3, .7]
dist.pdf(x)  # Shape [3]

# a/b will be broadcast to [[1, 2, 3], [1, 2, 3]] to match x.
x = [[.1, .4, .5], [.2, .3, .5]]
dist.pdf(x)  # Shape [2, 3]

# a/b will be broadcast to shape [5, 7, 3] to match x.
x = [[...]]  # Shape [5, 7, 3]
dist.pdf(x)  # Shape [5, 7, 3]
```

Creates a 2-batch of 3-class distributions.

```python
a = [[1, 2, 3], [4, 5, 6]]  # Shape [2, 3]
b = 5  # Shape []
dist = Beta(a, b)

# x will be broadcast to [[.2, .3, .9], [.2, .3, .9]] to match a/b.
x = [.2, .3, .9]
dist.pdf(x)  # Shape [2]
```
- - -

#### `tf.contrib.distributions.Beta.__init__(a, b, validate_args=False, allow_nan_stats=True, name='Beta')` {#Beta.__init__}

Initialize a batch of Beta distributions.

##### Args:


*  <b>`a`</b>: Positive floating point tensor with shape broadcastable to
    `[N1,..., Nm]` `m >= 0`.  Defines this as a batch of `N1 x ... x Nm`
     different Beta distributions. This also defines the
     dtype of the distribution.
*  <b>`b`</b>: Positive floating point tensor with shape broadcastable to
    `[N1,..., Nm]` `m >= 0`.  Defines this as a batch of `N1 x ... x Nm`
     different Beta distributions.
*  <b>`validate_args`</b>: `Boolean`, default `False`.  Whether to assert valid
    values for parameters `a`, `b`, and `x` in `prob` and `log_prob`.
    If `False` and inputs are invalid, correct behavior is not guaranteed.
*  <b>`allow_nan_stats`</b>: `Boolean`, default `True`.  If `False`, raise an
    exception if a statistic (e.g. mean/mode/etc...) is undefined for any
    batch member.  If `True`, batch members with valid parameters leading to
    undefined statistics will return NaN for this statistic.
*  <b>`name`</b>: The name to prefix Ops created by this distribution class.


*  <b>`Examples`</b>: 

```python
# Define 1-batch.
dist = Beta(1.1, 2.0)

# Define a 2-batch.
dist = Beta([1.0, 2.0], [4.0, 5.0])
```


- - -

#### `tf.contrib.distributions.Beta.a` {#Beta.a}

Shape parameter.


- - -

#### `tf.contrib.distributions.Beta.a_b_sum` {#Beta.a_b_sum}

Sum of parameters.


- - -

#### `tf.contrib.distributions.Beta.allow_nan_stats` {#Beta.allow_nan_stats}

Python boolean describing behavior when a stat is undefined.

Stats return +/- infinity when it makes sense.  E.g., the variance
of a Cauchy distribution is infinity.  However, sometimes the
statistic is undefined, e.g., if a distribution's pdf does not achieve a
maximum within the support of the distribution, the mode is undefined.
If the mean is undefined, then by definition the variance is undefined.
E.g. the mean for Student's T for df = 1 is undefined (no clear way to say
it is either + or - infinity), so the variance = E[(X - mean)^2] is also
undefined.

##### Returns:


*  <b>`allow_nan_stats`</b>: Python boolean.


- - -

#### `tf.contrib.distributions.Beta.b` {#Beta.b}

Shape parameter.


- - -

#### `tf.contrib.distributions.Beta.batch_shape(name='batch_shape')` {#Beta.batch_shape}

Shape of a single sample from a single event index as a 1-D `Tensor`.

The product of the dimensions of the `batch_shape` is the number of
independent distributions of this kind the instance represents.

##### Args:


*  <b>`name`</b>: name to give to the op

##### Returns:


*  <b>`batch_shape`</b>: `Tensor`.


- - -

#### `tf.contrib.distributions.Beta.cdf(value, name='cdf', **condition_kwargs)` {#Beta.cdf}

Cumulative distribution function.

Given random variable `X`, the cumulative distribution function `cdf` is:

```
cdf(x) := P[X <= x]
```

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`cdf`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.Beta.copy(**override_parameters_kwargs)` {#Beta.copy}

Creates a deep copy of the distribution.

Note: the copy distribution may continue to depend on the original
intialization arguments.

##### Args:


*  <b>`**override_parameters_kwargs`</b>: String/value dictionary of initialization
    arguments to override with new values.

##### Returns:


*  <b>`distribution`</b>: A new instance of `type(self)` intitialized from the union
    of self.parameters and override_parameters_kwargs, i.e.,
    `dict(self.parameters, **override_parameters_kwargs)`.


- - -

#### `tf.contrib.distributions.Beta.dtype` {#Beta.dtype}

The `DType` of `Tensor`s handled by this `Distribution`.


- - -

#### `tf.contrib.distributions.Beta.entropy(name='entropy')` {#Beta.entropy}

Shannon entropy in nats.


- - -

#### `tf.contrib.distributions.Beta.event_shape(name='event_shape')` {#Beta.event_shape}

Shape of a single sample from a single batch as a 1-D int32 `Tensor`.

##### Args:


*  <b>`name`</b>: name to give to the op

##### Returns:


*  <b>`event_shape`</b>: `Tensor`.


- - -

#### `tf.contrib.distributions.Beta.get_batch_shape()` {#Beta.get_batch_shape}

Shape of a single sample from a single event index as a `TensorShape`.

Same meaning as `batch_shape`. May be only partially defined.

##### Returns:


*  <b>`batch_shape`</b>: `TensorShape`, possibly unknown.


- - -

#### `tf.contrib.distributions.Beta.get_event_shape()` {#Beta.get_event_shape}

Shape of a single sample from a single batch as a `TensorShape`.

Same meaning as `event_shape`. May be only partially defined.

##### Returns:


*  <b>`event_shape`</b>: `TensorShape`, possibly unknown.


- - -

#### `tf.contrib.distributions.Beta.is_continuous` {#Beta.is_continuous}




- - -

#### `tf.contrib.distributions.Beta.is_reparameterized` {#Beta.is_reparameterized}




- - -

#### `tf.contrib.distributions.Beta.log_cdf(value, name='log_cdf', **condition_kwargs)` {#Beta.log_cdf}

Log cumulative distribution function.

Given random variable `X`, the cumulative distribution function `cdf` is:

```
log_cdf(x) := Log[ P[X <= x] ]
```

Often, a numerical approximation can be used for `log_cdf(x)` that yields
a more accurate answer than simply taking the logarithm of the `cdf` when
`x << -1`.


Additional documentation from `Beta`:

Note that the argument `x` must be a non-negative floating point tensor
whose shape can be broadcast with `self.a` and `self.b`.  For fixed leading
dimensions, the last dimension represents counts for the corresponding Beta
distribution in `self.a` and `self.b`. `x` is only legal if `0 < x < 1`.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`logcdf`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.Beta.log_pdf(value, name='log_pdf', **condition_kwargs)` {#Beta.log_pdf}

Log probability density function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`log_prob`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.

##### Raises:


*  <b>`TypeError`</b>: if not `is_continuous`.


- - -

#### `tf.contrib.distributions.Beta.log_pmf(value, name='log_pmf', **condition_kwargs)` {#Beta.log_pmf}

Log probability mass function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`log_pmf`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.

##### Raises:


*  <b>`TypeError`</b>: if `is_continuous`.


- - -

#### `tf.contrib.distributions.Beta.log_prob(value, name='log_prob', **condition_kwargs)` {#Beta.log_prob}

Log probability density/mass function (depending on `is_continuous`).

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`log_prob`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.Beta.log_survival_function(value, name='log_survival_function', **condition_kwargs)` {#Beta.log_survival_function}

Log survival function.

Given random variable `X`, the survival function is defined:

```
log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
```

Typically, different numerical approximations can be used for the log
survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:

  `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type
    `self.dtype`.


- - -

#### `tf.contrib.distributions.Beta.mean(name='mean')` {#Beta.mean}

Mean.


- - -

#### `tf.contrib.distributions.Beta.mode(name='mode')` {#Beta.mode}

Mode.

Additional documentation from `Beta`:

Note that the mode for the Beta distribution is only defined
when `a > 1`, `b > 1`. This returns the mode when `a > 1` and `b > 1`,
and `NaN` otherwise. If `self.allow_nan_stats` is `False`, an exception
will be raised rather than returning `NaN`.


- - -

#### `tf.contrib.distributions.Beta.name` {#Beta.name}

Name prepended to all ops created by this `Distribution`.


- - -

#### `tf.contrib.distributions.Beta.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#Beta.param_shapes}

Shapes of parameters given the desired shape of a call to `sample()`.

Subclasses should override static method `_param_shapes`.

##### Args:


*  <b>`sample_shape`</b>: `Tensor` or python list/tuple. Desired shape of a call to
    `sample()`.
*  <b>`name`</b>: name to prepend ops with.

##### Returns:

  `dict` of parameter name to `Tensor` shapes.


- - -

#### `tf.contrib.distributions.Beta.param_static_shapes(cls, sample_shape)` {#Beta.param_static_shapes}

param_shapes with static (i.e. TensorShape) shapes.

##### Args:


*  <b>`sample_shape`</b>: `TensorShape` or python list/tuple. Desired shape of a call
    to `sample()`.

##### Returns:

  `dict` of parameter name to `TensorShape`.

##### Raises:


*  <b>`ValueError`</b>: if `sample_shape` is a `TensorShape` and is not fully defined.


- - -

#### `tf.contrib.distributions.Beta.parameters` {#Beta.parameters}

Dictionary of parameters used to instantiate this `Distribution`.


- - -

#### `tf.contrib.distributions.Beta.pdf(value, name='pdf', **condition_kwargs)` {#Beta.pdf}

Probability density function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`prob`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.

##### Raises:


*  <b>`TypeError`</b>: if not `is_continuous`.


- - -

#### `tf.contrib.distributions.Beta.pmf(value, name='pmf', **condition_kwargs)` {#Beta.pmf}

Probability mass function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`pmf`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.

##### Raises:


*  <b>`TypeError`</b>: if `is_continuous`.


- - -

#### `tf.contrib.distributions.Beta.prob(value, name='prob', **condition_kwargs)` {#Beta.prob}

Probability density/mass function (depending on `is_continuous`).


Additional documentation from `Beta`:

Note that the argument `x` must be a non-negative floating point tensor
whose shape can be broadcast with `self.a` and `self.b`.  For fixed leading
dimensions, the last dimension represents counts for the corresponding Beta
distribution in `self.a` and `self.b`. `x` is only legal if `0 < x < 1`.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`prob`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.Beta.sample(sample_shape=(), seed=None, name='sample', **condition_kwargs)` {#Beta.sample}

Generate samples of the specified shape.

Note that a call to `sample()` without arguments will generate a single
sample.

##### Args:


*  <b>`sample_shape`</b>: 0D or 1D `int32` `Tensor`. Shape of the generated samples.
*  <b>`seed`</b>: Python integer seed for RNG
*  <b>`name`</b>: name to give to the op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`samples`</b>: a `Tensor` with prepended dimensions `sample_shape`.


- - -

#### `tf.contrib.distributions.Beta.sample_n(n, seed=None, name='sample_n', **condition_kwargs)` {#Beta.sample_n}

Generate `n` samples.

##### Args:


*  <b>`n`</b>: `Scalar` `Tensor` of type `int32` or `int64`, the number of
    observations to sample.
*  <b>`seed`</b>: Python integer seed for RNG
*  <b>`name`</b>: name to give to the op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`samples`</b>: a `Tensor` with a prepended dimension (n,).

##### Raises:


*  <b>`TypeError`</b>: if `n` is not an integer type.


- - -

#### `tf.contrib.distributions.Beta.std(name='std')` {#Beta.std}

Standard deviation.


- - -

#### `tf.contrib.distributions.Beta.survival_function(value, name='survival_function', **condition_kwargs)` {#Beta.survival_function}

Survival function.

Given random variable `X`, the survival function is defined:

```
survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).
```

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:

  Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type
    `self.dtype`.


- - -

#### `tf.contrib.distributions.Beta.validate_args` {#Beta.validate_args}

Python boolean indicated possibly expensive checks are enabled.


- - -

#### `tf.contrib.distributions.Beta.variance(name='variance')` {#Beta.variance}

Variance.


