# tf_agents.distributions.utils.SquashToSpecNormal

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|---|
| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L40-L184) |

Scales an input normalized action distribution to match spec bounds.

    tf_agents.distributions.utils.SquashToSpecNormal(
        distribution,
        spec,
        validate_args=False,
        name='SquashToSpecNormal'
    )

Unlike the normal distribution computed when NormalProjectionNetwork
is called with scale_distribution=False, which merely squashes the mean
of the distribution to within the action spec, this distribution scales the
output distribution to ensure that the output action fits within the spec.

This distribution also maintains the input normal distribution, and uses this
distribution to compute the KL-divergence between two SquashToSpecNormal
distributions provided that they were scaled by the same action spec.
This is possible as KL divergence is invariant when both distributions are
transformed using the same invertible function.

Formally, let a be the action magnitude and b be the action mean. The
squashing operation performs the following change of variables to the
input distribution X:

Y = a \* tanh(X) + b

Note that this is a change of variables as the function is invertible, with:

X = tan((Y - b) / a), where Y in (b - a, b + a)

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| ## Args ||
|---|---|
| `distribution` | input normal distribution with normalized mean and std dev |
| `spec` | bounded action spec from which to compute action ranges |
| `validate_args` | Python `bool`, default `False`. When `True` distribution parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs. |
| `name` | Python `str` name prefixed to Ops created by this class. |

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| ## Attributes ||
|---|---|
| `allow_nan_stats` | Python `bool` describing behavior when a stat is undefined. <br /> 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. |
| `batch_shape` | Shape of a single sample from a single event index as a `TensorShape`. <br /> May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. |
| `dtype` | The `DType` of `Tensor`s handled by this `Distribution`. |
| `event_shape` | Shape of a single sample from a single batch as a `TensorShape`. <br /> May be partially defined or unknown. |
| `experimental_shard_axis_names` | The list or structure of lists of active shard axis names. |
| `input_distribution` | The raw action distribution. |
| `parameters` | Dictionary of parameters used to instantiate this `Distribution`. |
| `reparameterization_type` | Describes how samples from the distribution are reparameterized. <br /> Currently this is one of the static instances `tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`. |
| `validate_args` | Python `bool` indicating possibly expensive checks are enabled. |

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## Methods

### `batch_shape_tensor`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L182-L184)

    batch_shape_tensor(
        name='batch_shape_tensor'
    )

Compute event shape tensor of the SquashToSpecNormal distribution.

### `cdf`

    cdf(
        value, name='cdf', **kwargs
    )

Cumulative distribution function.

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

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

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `cdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |

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### `copy`

    copy(
        **override_parameters_kwargs
    )

Creates a deep copy of the distribution.

> [!NOTE]
> **Note:** the copy distribution may continue to depend on the original initialization arguments.

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| Args ||
|---|---|
| `**override_parameters_kwargs` | String/value dictionary of initialization arguments to override with new values. |

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| Returns ||
|---|---|
| `distribution` | A new instance of `type(self)` initialized from the union of self.parameters and override_parameters_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`. |

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### `covariance`

    covariance(
        name='covariance', **kwargs
    )

Covariance.

Covariance is (possibly) defined only for non-scalar-event distributions.

For example, for a length-`k`, vector-valued distribution, it is calculated
as,

    Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]

where `Cov` is a (batch of) `k x k` matrix, `0 <= (i, j) < k`, and `E`
denotes expectation.

Alternatively, for non-vector, multivariate distributions (e.g.,
matrix-valued, Wishart), `Covariance` shall return a (batch of) matrices
under some vectorization of the events, i.e.,

    Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]

where `Cov` is a (batch of) `k' x k'` matrices,
`0 <= (i, j) < k' = reduce_prod(event_shape)`, and `Vec` is some function
mapping indices of this distribution's event dimensions to indices of a
length-`k'` vector.

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| Args ||
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `covariance` | Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']` where the first `n` dimensions are batch coordinates and `k' = reduce_prod(self.event_shape)`. |

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### `cross_entropy`

    cross_entropy(
        other, name='cross_entropy'
    )

Computes the (Shannon) cross entropy.

Denote this distribution (`self`) by `P` and the `other` distribution by
`Q`. Assuming `P, Q` are absolutely continuous with respect to
one another and permit densities `p(x) dr(x)` and `q(x) dr(x)`, (Shannon)
cross entropy is defined as:

    H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)

where `F` denotes the support of the random variable `X ~ P`.

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| Args ||
|---|---|
| `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. |
| `name` | Python `str` prepended to names of ops created by this function. |

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| Returns ||
|---|---|
| `cross_entropy` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of (Shannon) cross entropy. |

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### `entropy`

    entropy(
        name='entropy', **kwargs
    )

Shannon entropy in nats.

### `event_shape_tensor`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L178-L180)

    event_shape_tensor(
        name='event_shape_tensor'
    )

Compute event shape tensor of the SquashToSpecNormal distribution.

### `experimental_default_event_space_bijector`

    experimental_default_event_space_bijector(
        *args, **kwargs
    )

Bijector mapping the reals (R\*\*n) to the event space of the distribution.

Distributions with continuous support may implement
`_default_event_space_bijector` which returns a subclass of
[`tfp.bijectors.Bijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) that maps R\*\*n to the distribution's event space.
For example, the default bijector for the `Beta` distribution
is [`tfp.bijectors.Sigmoid()`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid), which maps the real line to `[0, 1]`, the
support of the `Beta` distribution. The default bijector for the
`CholeskyLKJ` distribution is [`tfp.bijectors.CorrelationCholesky`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky), which
maps R\^(k \* (k-1) // 2) to the submanifold of k x k lower triangular
matrices with ones along the diagonal.

The purpose of `experimental_default_event_space_bijector` is
to enable gradient descent in an unconstrained space for Variational
Inference and Hamiltonian Monte Carlo methods. Some effort has been made to
choose bijectors such that the tails of the distribution in the
unconstrained space are between Gaussian and Exponential.

For distributions with discrete event space, or for which TFP currently
lacks a suitable bijector, this function returns `None`.

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| Args ||
|---|---|
| `*args` | Passed to implementation `_default_event_space_bijector`. |
| `**kwargs` | Passed to implementation `_default_event_space_bijector`. |

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| Returns ||
|---|---|
| `event_space_bijector` | `Bijector` instance or `None`. |

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### `experimental_fit`

    @classmethod
    experimental_fit(
        value, sample_ndims=1, validate_args=False, **init_kwargs
    )

Instantiates a distribution that maximizes the likelihood of `x`.

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| Args ||
|---|---|
| `value` | a `Tensor` valid sample from this distribution family. |
| `sample_ndims` | Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. Default value: `1`. |
| `validate_args` | Python `bool`, default `False`. When `True`, distribution parameters are checked for validity despite possibly degrading runtime performance. When `False`, invalid inputs may silently render incorrect outputs. Default value: `False`. |
| `**init_kwargs` | Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`. |

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| Returns ||
|---|---|
| `maximum_likelihood_instance` | instance of `cls` with parameters that maximize the likelihood of `value`. |

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### `experimental_local_measure`

    experimental_local_measure(
        value, backward_compat=False, **kwargs
    )

Returns a log probability density together with a `TangentSpace`.

A `TangentSpace` allows us to calculate the correct push-forward
density when we apply a transformation to a `Distribution` on
a strict submanifold of R\^n (typically via a `Bijector` in the
`TransformedDistribution` subclass). The density correction uses
the basis of the tangent space.

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `backward_compat` | `bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R\^n with the standard basis. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `log_prob` | a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
| `tangent_space` | a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`. |

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| Raises ||
|---|---|
| UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined. ||

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### `experimental_sample_and_log_prob`

    experimental_sample_and_log_prob(
        sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs
    )

Samples from this distribution and returns the log density of the sample.

The default implementation simply calls `sample` and `log_prob`:

    def _sample_and_log_prob(self, sample_shape, seed, **kwargs):
      x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs)
      return x, self.log_prob(x, **kwargs)

However, some subclasses may provide more efficient and/or numerically
stable implementations.

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| Args ||
|---|---|
| `sample_shape` | integer `Tensor` desired shape of samples to draw. Default value: `()`. |
| `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. Default value: `None`. |
| `name` | name to give to the op. Default value: `'sample_and_log_prob'`. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `samples` | a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`. |
| `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |

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### `is_scalar_batch`

    is_scalar_batch(
        name='is_scalar_batch'
    )

Indicates that `batch_shape == []`.

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| Args ||
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |

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| Returns ||
|---|---|
| `is_scalar_batch` | `bool` scalar `Tensor`. |

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### `is_scalar_event`

    is_scalar_event(
        name='is_scalar_event'
    )

Indicates that `event_shape == []`.

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| Args ||
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |

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| Returns ||
|---|---|
| `is_scalar_event` | `bool` scalar `Tensor`. |

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### `kl_divergence`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L127-L147)

    kl_divergence(
        other, name='kl_divergence'
    )

Computes the KL Divergence between two SquashToSpecNormal distributions.

### `log_cdf`

    log_cdf(
        value, name='log_cdf', **kwargs
    )

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`.

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `logcdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |

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### `log_prob`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L153-L155)

    log_prob(
        value, name='log_prob'
    )

Computes log probability from the wrapped TransformedDistribution.

### `log_survival_function`

    log_survival_function(
        value, name='log_survival_function', **kwargs
    )

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`.

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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

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### `mean`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L174-L176)

    mean(
        name='mean', **kwargs
    )

Compute mean of the SquashToSpecNormal distribution.

### `mode`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L166-L172)

    mode(
        name='mode'
    )

Compute mean of the SquashToSpecNormal distribution.

### `param_shapes`

    @classmethod
    param_shapes(
        sample_shape, name='DistributionParamShapes'
    )

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

> [!WARNING]
> **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead.

This is a class method that describes what key/value arguments are required
to instantiate the given `Distribution` so that a particular shape is
returned for that instance's call to `sample()`.

Subclasses should override class method `_param_shapes`.

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| Args ||
|---|---|
| `sample_shape` | `Tensor` or python list/tuple. Desired shape of a call to `sample()`. |
| `name` | name to prepend ops with. |

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| Returns ||
|---|---|
| `dict` of parameter name to `Tensor` shapes. ||

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### `param_static_shapes`

    @classmethod
    param_static_shapes(
        sample_shape
    )

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

> [!WARNING]
> **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_static_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead.

This is a class method that describes what key/value arguments are required
to instantiate the given `Distribution` so that a particular shape is
returned for that instance's call to `sample()`. Assumes that the sample's
shape is known statically.

Subclasses should override class method `_param_shapes` to return
constant-valued tensors when constant values are fed.

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| Args ||
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| `sample_shape` | `TensorShape` or python list/tuple. Desired shape of a call to `sample()`. |

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| Returns ||
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| `dict` of parameter name to `TensorShape`. ||

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| Raises ||
|---|---|
| `ValueError` | if `sample_shape` is a `TensorShape` and is not fully defined. |

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### `parameter_properties`

    @classmethod
    parameter_properties(
        dtype=tf.float32, num_classes=None
    )

Returns a dict mapping constructor arg names to property annotations.

This dict should include an entry for each of the distribution's
`Tensor`-valued constructor arguments.

Distribution subclasses are not required to implement
`_parameter_properties`, so this method may raise `NotImplementedError`.
Providing a `_parameter_properties` implementation enables several advanced
features, including:

- Distribution batch slicing (`sliced_distribution = distribution[i:j]`).
- Automatic inference of `_batch_shape` and `_batch_shape_tensor`, which must otherwise be computed explicitly.
- Automatic instantiation of the distribution within TFP's internal property tests.
- Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference.

In the future, parameter property annotations may enable additional
functionality; for example, returning Distribution instances from
[`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/tf/vectorized_map).

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| Args ||
|---|---|
| `dtype` | Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed. |
| `num_classes` | Optional `int` `Tensor` number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored. |

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| Returns ||
|---|---|
| `parameter_properties` | A `str ->`tfp.python.internal.parameter_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. |

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| Raises ||
|---|---|
| `NotImplementedError` | if the distribution class does not implement `_parameter_properties`. |

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### `prob`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L157-L159)

    prob(
        value, name='prob'
    )

Computes probability from the wrapped TransformedDistribution.

### `quantile`

    quantile(
        value, name='quantile', **kwargs
    )

Quantile function. Aka 'inverse cdf' or 'percent point function'.

Given random variable `X` and `p in [0, 1]`, the `quantile` is:

    quantile(p) := x such that P[X <= x] == p

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `quantile` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |

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### `sample`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L149-L151)

    sample(
        sample_shape=(), seed=None, name='sample'
    )

Generates samples from the wrapped TransformedDistribution.

### `stddev`

[View source](https://github.com/tensorflow/agents/blob/v0.19.0/tf_agents/distributions/utils.py#L161-L164)

    stddev(
        name='stddev'
    )

Compute stddev of the SquashToSpecNormal distribution.

### `survival_function`

    survival_function(
        value, name='survival_function', **kwargs
    )

Survival function.

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

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

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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

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### `unnormalized_log_prob`

    unnormalized_log_prob(
        value, name='unnormalized_log_prob', **kwargs
    )

Potentially unnormalized log probability density/mass function.

This function is similar to `log_prob`, but does not require that the
return value be normalized. (Normalization here refers to the total
integral of probability being one, as it should be by definition for any
probability distribution.) This is useful, for example, for distributions
where the normalization constant is difficult or expensive to compute. By
default, this simply calls `log_prob`.

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| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `unnormalized_log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |

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### `variance`

    variance(
        name='variance', **kwargs
    )

Variance.

Variance is defined as,

    Var = E[(X - E[X])**2]

where `X` is the random variable associated with this distribution, `E`
denotes expectation, and `Var.shape = batch_shape + event_shape`.

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| Args ||
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |

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| Returns ||
|---|---|
| `variance` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. |

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### `__getitem__`

    __getitem__(
        slices
    )

Slices the batch axes of this distribution, returning a new instance.

    b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
    b.batch_shape  # => [3, 5, 7, 9]
    b2 = b[:, tf.newaxis, ..., -2:, 1::2]
    b2.batch_shape  # => [3, 1, 5, 2, 4]

    x = tf.random.normal([5, 3, 2, 2])
    cov = tf.matmul(x, x, transpose_b=True)
    chol = tf.linalg.cholesky(cov)
    loc = tf.random.normal([4, 1, 3, 1])
    mvn = tfd.MultivariateNormalTriL(loc, chol)
    mvn.batch_shape  # => [4, 5, 3]
    mvn.event_shape  # => [2]
    mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis]
    mvn2.batch_shape  # => [4, 2, 3, 1]
    mvn2.event_shape  # => [2]

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| Args ||
|---|---|
| `slices` | slices from the \[\] operator |

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| Returns ||
|---|---|
| `dist` | A new `tfd.Distribution` instance with sliced parameters. |

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### `__iter__`

    __iter__()