# tfp.experimental.substrates.numpy.bijectors.Weibull

Computes the Weibull CDF.

Inherits From: `WeibullCDF`

``````tfp.experimental.substrates.numpy.bijectors.Weibull(
scale=1.0, concentration=1.0, validate_args=False, name='weibull'
)
``````

#### Attributes:

• `concentration`: The `k` in `Y = g(X) = 1 - exp((-x / l) ** k)`.
• `dtype`: dtype of `Tensor`s transformable by this distribution.
• `forward_min_event_ndims`: Returns the minimal number of dimensions bijector.forward operates on.
• `graph_parents`: Returns this `Bijector`'s graph_parents as a Python list.
• `inverse_min_event_ndims`: Returns the minimal number of dimensions bijector.inverse operates on.
• `is_constant_jacobian`: Returns true iff the Jacobian matrix is not a function of x.

• `name`: Returns the string name of this `Bijector`.

• `scale`: The `l` in `Y = g(X) = 1 - exp((-x / l) ** k)`.

• `trainable_variables`

• `validate_args`: Returns True if Tensor arguments will be validated.

• `variables`

## Methods

### `__call__`

View source

``````__call__(
value, name=None, **kwargs
)
``````

Applies or composes the `Bijector`, depending on input type.

This is a convenience function which applies the `Bijector` instance in three different ways, depending on the input:

1. If the input is a `tfd.Distribution` instance, return `tfd.TransformedDistribution(distribution=input, bijector=self)`.
2. If the input is a `tfb.Bijector` instance, return `tfb.Chain([self, input])`.
3. Otherwise, return `self.forward(input)`

#### Args:

• `value`: A `tfd.Distribution`, `tfb.Bijector`, or a `Tensor`.
• `name`: Python `str` name given to ops created by this function.
• `**kwargs`: Additional keyword arguments passed into the created `tfd.TransformedDistribution`, `tfb.Bijector`, or `self.forward`.

#### Returns:

• `composition`: A `tfd.TransformedDistribution` if the input was a `tfd.Distribution`, a `tfb.Chain` if the input was a `tfb.Bijector`, or a `Tensor` computed by `self.forward`.

#### Examples

``````sigmoid = tfb.Reciprocal()(
tfb.AffineScalar(shift=1.)(
tfb.Exp()(
tfb.AffineScalar(scale=-1.))))
# ==> `tfb.Chain([
#         tfb.Reciprocal(),
#         tfb.AffineScalar(shift=1.),
#         tfb.Exp(),
#         tfb.AffineScalar(scale=-1.),
#      ])`  # ie, `tfb.Sigmoid()`

log_normal = tfb.Exp()(tfd.Normal(0, 1))
# ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())`

tfb.Exp()([-1., 0., 1.])
# ==> tf.exp([-1., 0., 1.])
``````

### `forward`

View source

``````forward(
x, name='forward', **kwargs
)
``````

Returns the forward `Bijector` evaluation, i.e., X = g(Y).

#### Args:

• `x`: `Tensor`. The input to the 'forward' evaluation.
• `name`: The name to give this op.
• `**kwargs`: Named arguments forwarded to subclass implementation.

#### Returns:

`Tensor`.

#### Raises:

• `TypeError`: if `self.dtype` is specified and `x.dtype` is not `self.dtype`.
• `NotImplementedError`: if `_forward` is not implemented.

### `forward_event_shape`

View source

``````forward_event_shape(
input_shape
)
``````

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

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

#### Args:

• `input_shape`: `TensorShape` indicating event-portion shape passed into `forward` function.

#### Returns:

• `forward_event_shape_tensor`: `TensorShape` indicating event-portion shape after applying `forward`. Possibly unknown.

### `forward_event_shape_tensor`

View source

``````forward_event_shape_tensor(
input_shape, name='forward_event_shape_tensor'
)
``````

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

#### Args:

• `input_shape`: `Tensor`, `int32` vector indicating event-portion shape passed into `forward` function.
• `name`: name to give to the op

#### Returns:

• `forward_event_shape_tensor`: `Tensor`, `int32` vector indicating event-portion shape after applying `forward`.

### `forward_log_det_jacobian`

View source

``````forward_log_det_jacobian(
x, event_ndims, name='forward_log_det_jacobian', **kwargs
)
``````

Returns both the forward_log_det_jacobian.

#### Args:

• `x`: `Tensor`. The input to the 'forward' Jacobian determinant evaluation.
• `event_ndims`: Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to `self.forward_min_event_ndims`. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape `rank(x) - event_ndims` dimensions.
• `name`: The name to give this op.
• `**kwargs`: Named arguments forwarded to subclass implementation.

#### Returns:

`Tensor`, if this bijector is injective. If not injective this is not implemented.

#### Raises:

• `TypeError`: if `self.dtype` is specified and `y.dtype` is not `self.dtype`.
• `NotImplementedError`: if neither `_forward_log_det_jacobian` nor {`_inverse`, `_inverse_log_det_jacobian`} are implemented, or this is a non-injective bijector.

### `inverse`

View source

``````inverse(
y, name='inverse', **kwargs
)
``````

Returns the inverse `Bijector` evaluation, i.e., X = g^{-1}(Y).

#### Args:

• `y`: `Tensor`. The input to the 'inverse' evaluation.
• `name`: The name to give this op.
• `**kwargs`: Named arguments forwarded to subclass implementation.

#### Returns:

`Tensor`, if this bijector is injective. If not injective, returns the k-tuple containing the unique `k` points `(x1, ..., xk)` such that `g(xi) = y`.

#### Raises:

• `TypeError`: if `self.dtype` is specified and `y.dtype` is not `self.dtype`.
• `NotImplementedError`: if `_inverse` is not implemented.

### `inverse_event_shape`

View source

``````inverse_event_shape(
output_shape
)
``````

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

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

#### Args:

• `output_shape`: `TensorShape` indicating event-portion shape passed into `inverse` function.

#### Returns:

• `inverse_event_shape_tensor`: `TensorShape` indicating event-portion shape after applying `inverse`. Possibly unknown.

### `inverse_event_shape_tensor`

View source

``````inverse_event_shape_tensor(
output_shape, name='inverse_event_shape_tensor'
)
``````

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

#### Args:

• `output_shape`: `Tensor`, `int32` vector indicating event-portion shape passed into `inverse` function.
• `name`: name to give to the op

#### Returns:

• `inverse_event_shape_tensor`: `Tensor`, `int32` vector indicating event-portion shape after applying `inverse`.

### `inverse_log_det_jacobian`

View source

``````inverse_log_det_jacobian(
y, event_ndims, name='inverse_log_det_jacobian', **kwargs
)
``````

Returns the (log o det o Jacobian o inverse)(y).

Mathematically, returns: `log(det(dX/dY))(Y)`. (Recall that: `X=g^{-1}(Y)`.)

Note that `forward_log_det_jacobian` is the negative of this function, evaluated at `g^{-1}(y)`.

#### Args:

• `y`: `Tensor`. The input to the 'inverse' Jacobian determinant evaluation.
• `event_ndims`: Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to `self.inverse_min_event_ndims`. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape `rank(y) - event_ndims` dimensions.
• `name`: The name to give this op.
• `**kwargs`: Named arguments forwarded to subclass implementation.

#### Returns:

• `ildj`: `Tensor`, if this bijector is injective. If not injective, returns the tuple of local log det Jacobians, `log(det(Dg_i^{-1}(y)))`, where `g_i` is the restriction of `g` to the `ith` partition `Di`.

#### Raises:

• `TypeError`: if `self.dtype` is specified and `y.dtype` is not `self.dtype`.
• `NotImplementedError`: if `_inverse_log_det_jacobian` is not implemented.