# gluonts.distribution.student_t module¶

class gluonts.distribution.student_t.StudentT(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], sigma: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], nu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], F=None)[source]

Student’s t-distribution.

Parameters: mu – Tensor containing the means, of shape (*batch_shape, *event_shape). sigma – Tensor containing the standard deviations, of shape (*batch_shape, *event_shape). nu – Nonnegative tensor containing the degrees of freedom of the distribution, of shape (*batch_shape, *event_shape). F –
batch_shape

Layout of the set of events contemplated by the distribution.

Invoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.

This property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.

event_dim

Number of event dimensions, i.e., length of the event_shape tuple.

This is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.

event_shape

Shape of each individual event contemplated by the distribution.

For example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.

Invoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.

This property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.

is_reparameterizable = False
log_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Compute the log-density of the distribution at x.

Parameters: x – Tensor of shape (*batch_shape, *event_shape). Tensor of shape batch_shape containing the log-density of the distribution for each event in x. Tensor
mean

Tensor containing the mean of the distribution.

sample(num_samples: Optional[int] = None) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Draw samples from the distribution.

If num_samples is given the first dimension of the output will be num_samples.

Returns: A tensor containing samples. This has shape (*batch_shape, *eval_shape) if num_samples = None and (num_samples, *batch_shape, *eval_shape) otherwise. Tensor
stddev

Tensor containing the standard deviation of the distribution.

class gluonts.distribution.student_t.StudentTOutput[source]
args_dim = {'mu': 1, 'nu': 1, 'sigma': 1}
distr_cls

alias of StudentT

classmethod domain_map(F, mu, sigma, nu)[source]

Converts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.

event_shape

Shape of each individual event contemplated by the distributions that this object constructs.