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.)
Properties
Public properties
object allow_nan_stats get;
object allow_nan_stats_dyn get;
TensorShape batch_shape get;
object batch_shape_dyn get;
object dtype get;
object dtype_dyn get;
TensorShape event_shape get;
object event_shape_dyn get;
object loc get;
Distribution parameter for the mean.
object loc_dyn get;
Distribution parameter for the mean.
string name get;
object name_dyn get;
IDictionary<object, object> parameters get;
object parameters_dyn get;
object PythonObject get;
object reparameterization_type get;
object reparameterization_type_dyn get;
object scale get;
Distribution parameter for standard deviation.
object scale_dyn get;
Distribution parameter for standard deviation.