gluonts.mx.model.tpp.distribution.weibull module#

class gluonts.mx.model.tpp.distribution.weibull.Weibull(rate: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], shape: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]#

Bases: gluonts.mx.model.tpp.distribution.base.TPPDistribution

Weibull distribution.

We use the parametrization of the Weibull distribution using the rate parameter \(b > 0\) and the shape parameter \(k > 0\). The PDF is \(p(x) = b * k * x^{(k - 1)} * \exp(-b * x^k)\). An alternative parametrization is often used (e.g. on Wikipedia), where we use the scale parameter \(\lambda > 0\) and the shape parameter \(k > 0\), and \(\lambda = b^{-1/k}\).

arg_names: Tuple#
property batch_shape: Tuple#

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.

property event_dim: int#

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.

property event_shape: Tuple#

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_reparametrizable = True#
log_intensity(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]#

Logarithm of the intensity (a.k.a. hazard) function.

The intensity is defined as \(\lambda(x) = p(x) / S(x)\).

The intensity of the Weibull distribution is \(\lambda(x) = b * k * x^{k - 1}\).

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).

Returns

Tensor of shape batch_shape containing the log-density of the distribution for each event in x.

Return type

Tensor

log_survival(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]#

Logarithm of the survival function.

\(\log S(x) = \log(1 - CDF(x))\).

The survival function of the Weibull distribution is \(S(x) = \exp(-b * x^k)\).

property mean: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]#

Tensor containing the mean of the distribution.

sample(num_samples=None, dtype=<class 'numpy.float32'>, lower_bound: typing.Optional[typing.Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]] = None) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]#

Draw samples from the distribution.

We generate samples as \(u \sim Uniform(0, 1), x = S^{-1}(u)\), where \(S^{-1}\) is the inverse of the survival function \(S(x) = 1 - CDF(x)\).

Parameters

  • num_samples – Number of samples to generate.

  • dtype – Data type of the generated samples.

  • lower_bound – If None, generate samples as usual. If lower_bound is provided, all generated samples will be larger than the specified values. That is, we sample from p(x | x > lower_bound). Shape: (*batch_size)

Returns

Sampled inter-event times. Shape: (num_samples, *batch_size)

Return type

x

class gluonts.mx.model.tpp.distribution.weibull.WeibullOutput[source]#

Bases: gluonts.mx.model.tpp.distribution.base.TPPDistributionOutput

args_dim: Dict[str, int] = {'rate': 1, 'shape': 1}#
distr_cls#

alias of gluonts.mx.model.tpp.distribution.weibull.Weibull

classmethod domain_map(F, rate, shape)[source]#

Maps raw tensors to valid arguments for constructing a Weibull distribution.

Parameters

  • F – MXNet backend.

  • rate – Rate (inverse scale) parameter of the Weibull distribution. Shape (*batch_shape, 1)

  • shape – Shape parameter of the Weibull distribution. Shape (*batch_shape, 1)

Returns

Two squeezed tensors of shape (*batch_shape). Both tensors are strictly positive.

Return type

Tuple[Tensor, Tensor]

property event_shape: Tuple#

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