# LostTech.TensorFlow : API Documentation

Type Cauchy

Namespace tensorflow.contrib.distributions

Parent Distribution

Interfaces ICauchy

The Cauchy distribution with location `loc` and scale `scale`.

#### Mathematical details

The probability density function (pdf) is,

```none pdf(x; loc, scale) = 1 / (pi scale (1 + z**2)) z = (x - loc) / scale ``` where `loc` is the location, and `scale` is the scale.

The Cauchy distribution is a member of the [location-scale family]( https://en.wikipedia.org/wiki/Location-scale_family), i.e. `Y ~ Cauchy(loc, scale)` is equivalent to,

```none X ~ Cauchy(loc=0, scale=1) Y = loc + scale * X ```

#### Examples

Examples of initialization of one or a batch of distributions.
Show Example
```import tensorflow_probability as tfp
tfd = tfp.distributions  # Define a single scalar Cauchy distribution.
dist = tfd.Cauchy(loc=0., scale=3.)  # Evaluate the cdf at 1, returning a scalar.
dist.cdf(1.)  # Define a batch of two scalar valued Cauchy distributions.
dist = tfd.Cauchy(loc=[1, 2.], scale=[11, 22.])  # Evaluate the pdf of the first distribution on 0, and the second on 1.5,
# returning a length two tensor.
dist.prob([0, 1.5])  # Get 3 samples, returning a 3 x 2 tensor.
dist.sample([3])  # Arguments are broadcast when possible.
# Define a batch of two scalar valued Cauchy distributions.
# Both have median 1, but different scales.
dist = tfd.Cauchy(loc=1., scale=[11, 22.])  # Evaluate the pdf of both distributions on the same point, 3.0,
# returning a length 2 tensor.
dist.prob(3.) ```

### Public properties

#### objectloc get;

Distribution parameter for the mean.

#### objectloc_dyn get;

Distribution parameter for the mean.

#### objectscale get;

Distribution parameter for standard deviation.

#### objectscale_dyn get;

Distribution parameter for standard deviation.