tfp.experimental.substrates.numpy.distributions.Weibull

The Weibull distribution with 'concentration' and scale parameters.

Inherits From: TransformedDistribution, Distribution

Mathematical details

The probability density function (pdf) of this distribution is,

pdf(x; lambda, k) =
  k / lambda * (x / lambda) ** (k - 1) * exp(-(x / lambda) ** k)

where concentration = k and scale = lambda.

The cumulative density function of this distribution is,

cdf(x; lambda, k) = 1 - exp(-(x / lambda) ** k)

The Weibull distribution includes the Exponential and Rayleigh distributions as special cases:

Exponential(rate) = Weibull(concentration=1., 1. / rate)

Rayleigh(scale) = Weibull(concentration=2., sqrt(2.) * scale)

Examples

Example of initialization of one distribution.

tfd = tfp.distributions

# Define a single scalar Weibull distribution.
dist = tfd.Weibull(concentration=1., scale=3.)

# Evaluate the cdf at 1, returning a scalar.
dist.cdf(1.)

Example of initialization of a 3-batch of distributions with varying scales and concentrations.

tfd = tfp.distributions

# Define a 3-batch of Weibull distributions.
scale = [1., 3., 45.]
concentration = [2.5, 22., 7.]
dist = tfd.Weibull(concentration=concentration, scale=scale)

# Evaluate the cdfs at 1.
dist.cdf(1.)    # shape: [3]
```

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<tr><th colspan="2"><h2 class="add-link">Args</h2></th></tr>

<tr>
<td>
`concentration`
</td>
<td>
Positive Float-type `Tensor`, the concentration param of the
distribution. Must contain only positive values.
</td>
</tr><tr>
<td>
`scale`
</td>
<td>
Positive Float-type `Tensor`, the scale param of the distribution.
Must contain only positive values.
</td>
</tr><tr>
<td>
`validate_args`
</td>
<td>
Python `bool` indicating whether arguments should be checked
for correctness.
</td>
</tr><tr>
<td>
`allow_nan_stats`
</td>
<td>
Python `bool` indicating whether nan values should be
allowed.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` name given to ops managed by this class.
Default value: `'Weibull'`.
</td>
</tr>
</table>



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<tr><th colspan="2"><h2 class="add-link">Raises</h2></th></tr>

<tr>
<td>
`TypeError`
</td>
<td>
if concentration and scale are different dtypes.
</td>
</tr>
</table>





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<tr><th colspan="2"><h2 class="add-link">Attributes</h2></th></tr>

<tr>
<td>
`allow_nan_stats`
</td>
<td>
Python `bool` 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.
</td>
</tr><tr>
<td>
`batch_shape`
</td>
<td>
Shape of a single sample from a single event index as a `TensorShape`.

May be partially defined or unknown.

The batch dimensions are indexes into independent, non-identical
parameterizations of this distribution.
</td>
</tr><tr>
<td>
`bijector`
</td>
<td>
Function transforming x => y.
</td>
</tr><tr>
<td>
`concentration`
</td>
<td>
Distribution parameter for the concentration.
</td>
</tr><tr>
<td>
`distribution`
</td>
<td>
Base distribution, p(x).
</td>
</tr><tr>
<td>
`dtype`
</td>
<td>
The `DType` of `Tensor`s handled by this `Distribution`.
</td>
</tr><tr>
<td>
`event_shape`
</td>
<td>
Shape of a single sample from a single batch as a `TensorShape`.

May be partially defined or unknown.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Name prepended to all ops created by this `Distribution`.
</td>
</tr><tr>
<td>
`parameters`
</td>
<td>
Dictionary of parameters used to instantiate this `Distribution`.
</td>
</tr><tr>
<td>
`reparameterization_type`
</td>
<td>
Describes how samples from the distribution are reparameterized.

Currently this is one of the static instances
`tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`.
</td>
</tr><tr>
<td>
`scale`
</td>
<td>
Distribution parameter for scale.
</td>
</tr><tr>
<td>
`trainable_variables`
</td>
<td>

</td>
</tr><tr>
<td>
`validate_args`
</td>
<td>
Python `bool` indicating possibly expensive checks are enabled.
</td>
</tr><tr>
<td>
`variables`
</td>
<td>

</td>
</tr>
</table>



## Methods

<h3 id="batch_shape_tensor"><code>batch_shape_tensor</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L772-L805">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>batch_shape_tensor(
    name='batch_shape_tensor'
)
</code></pre>

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

The batch dimensions are indexes into independent, non-identical
parameterizations of this distribution.

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<tr>
<td>
`name`
</td>
<td>
name to give to the op
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`batch_shape`
</td>
<td>
`Tensor`.
</td>
</tr>
</table>



<h3 id="cdf"><code>cdf</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1037-L1055">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>cdf(
    value, name='cdf', **kwargs
)
</code></pre>

Cumulative distribution function.

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

```none
cdf(x) := P[X <= x]
```

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<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



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<tr>
<td>
`cdf`
</td>
<td>
a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
values of type `self.dtype`.
</td>
</tr>
</table>



<h3 id="copy"><code>copy</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L738-L766">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>copy(
    **override_parameters_kwargs
)
</code></pre>

Creates a deep copy of the distribution.

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

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<tr>
<td>
`**override_parameters_kwargs`
</td>
<td>
String/value dictionary of initialization
arguments to override with new values.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`distribution`
</td>
<td>
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)`.
</td>
</tr>
</table>



<h3 id="covariance"><code>covariance</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1266-L1304">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>covariance(
    name='covariance', **kwargs
)
</code></pre>

Covariance.

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

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

```none
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.,

```none
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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<tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`covariance`
</td>
<td>
Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']`
where the first `n` dimensions are batch coordinates and
`k' = reduce_prod(self.event_shape)`.
</td>
</tr>
</table>



<h3 id="cross_entropy"><code>cross_entropy</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1319-L1342">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>cross_entropy(
    other, name='cross_entropy'
)
</code></pre>

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:

```none
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`.

`other` types with built-in registrations: `Weibull`

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<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`other`
</td>
<td>
<a href="../../../../../tfp/distributions/Distribution"><code>tfp.distributions.Distribution</code></a> instance.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`cross_entropy`
</td>
<td>
`self.dtype` `Tensor` with shape `[B1, ..., Bn]`
representing `n` different calculations of (Shannon) cross entropy.
</td>
</tr>
</table>



<h3 id="entropy"><code>entropy</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1144-L1147">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>entropy(
    name='entropy', **kwargs
)
</code></pre>

Shannon entropy in nats.


<h3 id="event_shape_tensor"><code>event_shape_tensor</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L837-L859">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>event_shape_tensor(
    name='event_shape_tensor'
)
</code></pre>

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


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<tr>
<td>
`name`
</td>
<td>
name to give to the op
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`event_shape`
</td>
<td>
`Tensor`.
</td>
</tr>
</table>



<h3 id="is_scalar_batch"><code>is_scalar_batch</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L890-L902">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>is_scalar_batch(
    name='is_scalar_batch'
)
</code></pre>

Indicates that `batch_shape == []`.


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<tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`is_scalar_batch`
</td>
<td>
`bool` scalar `Tensor`.
</td>
</tr>
</table>



<h3 id="is_scalar_event"><code>is_scalar_event</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L876-L888">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>is_scalar_event(
    name='is_scalar_event'
)
</code></pre>

Indicates that `event_shape == []`.


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<tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`is_scalar_event`
</td>
<td>
`bool` scalar `Tensor`.
</td>
</tr>
</table>



<h3 id="kl_divergence"><code>kl_divergence</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1348-L1379">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>kl_divergence(
    other, name='kl_divergence'
)
</code></pre>

Computes the Kullback--Leibler divergence.

Denote this distribution (`self`) by `p` and the `other` distribution by
`q`. Assuming `p, q` are absolutely continuous with respect to reference
measure `r`, the KL divergence is defined as:

```none
KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
```

where `F` denotes the support of the random variable `X ~ p`, `H[., .]`
denotes (Shannon) cross entropy, and `H[.]` denotes (Shannon) entropy.

`other` types with built-in registrations: `Weibull`

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<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`other`
</td>
<td>
<a href="../../../../../tfp/distributions/Distribution"><code>tfp.distributions.Distribution</code></a> instance.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`kl_divergence`
</td>
<td>
`self.dtype` `Tensor` with shape `[B1, ..., Bn]`
representing `n` different calculations of the Kullback-Leibler
divergence.
</td>
</tr>
</table>



<h3 id="log_cdf"><code>log_cdf</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1002-L1024">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>log_cdf(
    value, name='log_cdf', **kwargs
)
</code></pre>

Log cumulative distribution function.

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

```none
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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<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`logcdf`
</td>
<td>
a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
values of type `self.dtype`.
</td>
</tr>
</table>



<h3 id="log_prob"><code>log_prob</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L952-L964">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>log_prob(
    value, name='log_prob', **kwargs
)
</code></pre>

Log probability density/mass function.


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<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`log_prob`
</td>
<td>
a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
values of type `self.dtype`.
</td>
</tr>
</table>



<h3 id="log_survival_function"><code>log_survival_function</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1075-L1099">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>log_survival_function(
    value, name='log_survival_function', **kwargs
)
</code></pre>

Log survival function.

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

```none
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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<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



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<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type
`self.dtype`.
</td>
</tr>

</table>



<h3 id="mean"><code>mean</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1153-L1156">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>mean(
    name='mean', **kwargs
)
</code></pre>

Mean.


<h3 id="mode"><code>mode</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1310-L1313">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>mode(
    name='mode', **kwargs
)
</code></pre>

Mode.


<h3 id="param_shapes"><code>param_shapes</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L558-L577">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>@classmethod</code>
<code>param_shapes(
    sample_shape, name='DistributionParamShapes'
)
</code></pre>

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

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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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

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



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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`dict` of parameter name to `Tensor` shapes.
</td>
</tr>

</table>



<h3 id="param_static_shapes"><code>param_static_shapes</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L579-L616">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>@classmethod</code>
<code>param_static_shapes(
    sample_shape
)
</code></pre>

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

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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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`sample_shape`
</td>
<td>
`TensorShape` or python list/tuple. Desired shape of a call
to `sample()`.
</td>
</tr>
</table>



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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`dict` of parameter name to `TensorShape`.
</td>
</tr>

</table>



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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Raises</th></tr>

<tr>
<td>
`ValueError`
</td>
<td>
if `sample_shape` is a `TensorShape` and is not fully defined.
</td>
</tr>
</table>



<h3 id="prob"><code>prob</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L977-L989">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>prob(
    value, name='prob', **kwargs
)
</code></pre>

Probability density/mass function.


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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`prob`
</td>
<td>
a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
values of type `self.dtype`.
</td>
</tr>
</table>



<h3 id="quantile"><code>quantile</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1175-L1193">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>quantile(
    value, name='quantile', **kwargs
)
</code></pre>

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

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

```none
quantile(p) := x such that P[X <= x] == p
```

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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`quantile`
</td>
<td>
a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
values of type `self.dtype`.
</td>
</tr>
</table>



<h3 id="sample"><code>sample</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L924-L939">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>sample(
    sample_shape=(), seed=None, name='sample', **kwargs
)
</code></pre>

Generate samples of the specified shape.

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

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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`sample_shape`
</td>
<td>
0D or 1D `int32` `Tensor`. Shape of the generated samples.
</td>
</tr><tr>
<td>
`seed`
</td>
<td>
Python integer or <a href="../../../../../tfp/util/SeedStream"><code>tfp.util.SeedStream</code></a> instance, for seeding PRNG.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
name to give to the op.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`samples`
</td>
<td>
a `Tensor` with prepended dimensions `sample_shape`.
</td>
</tr>
</table>



<h3 id="stddev"><code>stddev</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1232-L1260">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>stddev(
    name='stddev', **kwargs
)
</code></pre>

Standard deviation.

Standard deviation is defined as,

```none
stddev = E[(X - E[X])**2]**0.5
```

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

<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`stddev`
</td>
<td>
Floating-point `Tensor` with shape identical to
`batch_shape + event_shape`, i.e., the same shape as `self.mean()`.
</td>
</tr>
</table>



<h3 id="survival_function"><code>survival_function</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1118-L1138">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>survival_function(
    value, name='survival_function', **kwargs
)
</code></pre>

Survival function.

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

```none
survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).
```

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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`value`
</td>
<td>
`float` or `double` `Tensor`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type
`self.dtype`.
</td>
</tr>

</table>



<h3 id="variance"><code>variance</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L1199-L1226">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>variance(
    name='variance', **kwargs
)
</code></pre>

Variance.

Variance is defined as,

```none
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`.

<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`name`
</td>
<td>
Python `str` prepended to names of ops created by this function.
</td>
</tr><tr>
<td>
`**kwargs`
</td>
<td>
Named arguments forwarded to subclass implementation.
</td>
</tr>
</table>



<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`variance`
</td>
<td>
Floating-point `Tensor` with shape identical to
`batch_shape + event_shape`, i.e., the same shape as `self.mean()`.
</td>
</tr>
</table>



<h3 id="__getitem__"><code>__getitem__</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/transformed_distribution.py#L288-L305">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>__getitem__(
    slices
)
</code></pre>

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

```python
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.stateless_normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.cholesky(cov)
loc = tf.random.stateless_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]
```

<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>

<tr>
<td>
`slices`
</td>
<td>
slices from the [] operator
</td>
</tr>
</table>



<!-- Tabular view -->
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<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>

<tr>
<td>
`dist`
</td>
<td>
A new `tfd.Distribution` instance with sliced parameters.
</td>
</tr>
</table>



<h3 id="__iter__"><code>__iter__</code></h3>

<a target="_blank" href="https://github.com/tensorflow/probability/blob/v0.11.1/tensorflow_probability/python/distributions/_numpy/distribution.py#L701-L702">View source</a>

<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>__iter__()
</code></pre>