def poisson(self, n, lam):
r"""
The continous approximation, using :math:`n! = \Gamma\left(n+1\right)`,
to the probability mass function of the Poisson distribution evaluated
at :code:`n` given the parameter :code:`lam`.
Example:
>>> import pyhf
>>> pyhf.set_backend(pyhf.tensor.mxnet_backend())
>>> pyhf.tensorlib.poisson(5., 6.)
<BLANKLINE>
[0.16062315]
<NDArray 1 @cpu(0)>
Args:
n (Number or Tensor): The value at which to evaluate the approximation to the Poisson distribution p.m.f.
(the observed number of events)
lam (Number or Tensor): The mean of the Poisson distribution p.d.f.
(the expected number of events)
Returns:
MXNet NDArray: Value of the continous approximation to Poisson(n|lam)
"""
n = self.astensor(n)
lam = self.astensor(lam)
# This is currently copied directly from PyTorch's source until a better
# way can be found to do this in MXNet
# https://github.com/pytorch/pytorch/blob/39520ffec15ab7e97691fed048de1832e83785e8/torch/distributions/poisson.py#L59-L63
return nd.exp((nd.log(lam) * n) - lam - nd.gammaln(n + 1.0))
def log_prob(self, x: nd.NDArray) -> nd.NDArray:
mean = self.get_param_maybe_repeated('mean')
if x.ndim > mean.ndim:
mean = nd.expand_dims(mean, 0)
np_x = x.asnumpy().astype(np.int32).astype(np.float32)
np.testing.assert_almost_equal(x.asnumpy(), np_x)
return x * nd.log(mean) - mean - nd.gammaln(x + 1.)
def poisson_logpdf(self, n, lam):
n = self.astensor(n)
lam = self.astensor(lam)
return n * nd.log(lam) - lam - nd.gammaln(n + 1.0)
