Poisson

Data Type: int

The Poisson distribution is used to model counts. The probability mass function is given by

\[f(x | \lambda) = \frac{\lambda^{x}e^{-x}}{x!}, \; 0 \leq x.\]

For more info see Poisson Distribution.

PoissonDistribution

class dml.stats.poisson.PoissonDistribution(lam, name=None, keys=None)

PoissonDistribution object defining Poisson distribution with mean lam > 0.0.

lam

Mean of Poisson distribution.

Type:: float

name

String name for object instance.

Type:: Optional[str]

log_lambda

Log of attribute lam.

Type:: float

keys

Keys for lambda.

Type:: Optional[str]

__init__(lam, name=None, keys=None)

PoissonDistribution object.

Parameters:

lam (float) – Positive real-valued number.
name (Optional[str]) – String name for object instance.
keys (Optional[str]) – Key for lambda.

density(x)

Evaluate the density of Poisson distribution at observation x.

Notes

See log_density().

Parameters:: x (int) – Must be a non-negative integer value (0,1,2,….).
Returns:: Density of Poisson distribution evaluated at x.
Return type:: float

dist_to_encoder()

Create DataSequenceEncoder object for SequenceEncodableProbabilityDistribution instance.

Return type:: PoissonDataEncoder
Returns:: DataSequenceEncoder

estimator(pseudo_count=None)

Create a ParameterEstimator for corresponding SequenceEncodableProbabilityDistribution.

Parameters:: pseudo_count (Optional[float]) – Regularize sufficient statistics in estimation step.
Return type:: PoissonEstimator
Returns:: ParameterEstimator

log_density(x)

Log-density of Poisson distribution evaluated at x.

\[\log{f(x | \lambda)} = -x \log{\lambda} - \log{x!} - \lambda.\]

Parameters:: x (int) – Must be a non-negative integer value (0,1,2,….).
Returns:: Log-density of Poisson distribution evaluated at x.
Return type:: float

sampler(seed=None)

Create a DistributionSampler object for a given ProbabilityDistribution.

Parameters:: seed (Optional[int]) – Set seed for drawing samples from distribution.
Return type:: PoissonSampler

seq_log_density(x)

Vectorized evaluation of the log density.

Parameters:: x (EncodedDataSequence) – EncodedDataSequence for corresponding SequenceEncodedProbabilityDistribution.
Return type:: ndarray
Returns:: np.ndarray

PoissonEstimator

class dml.stats.poisson.PoissonEstimator(pseudo_count=None, suff_stat=None, name=None, keys=None)

PoissonEstimator object for estimating PoissonDistribution object from aggregated sufficient statistics.

pseudo_count

Re-weight suff_stat.

Type:: Optional[float]

suff_stat

Mean of Poisson if not None.

Type:: Optional[float]

name

String name of PoissonEstimator instance.

Type:: Optional[str]

keys

String keys of PoissonEstimator instance for combining sufficient statistics.

Type:: Optional[str]

__init__(pseudo_count=None, suff_stat=None, name=None, keys=None)

PoissonEstimator object.

Parameters:

pseudo_count (Optional[float]) – Optional non-negative float.
suff_stat (Optional[float]) – Optional non-negative float.
name (Optional[str]) – Assign a name to PoissonEstimator.
keys (Optional[str]) – Assign keys to PoissonEstimator for combining sufficient statistics.

accumulator_factory()

Create SequenceEncodableStatisticAccumulator object.

Return type:: PoissonAccumulatorFactory

estimate(nobs, suff_stat)

Estimate SequenceEncodableProbabilityDistribution for sufficient statistics.

Parameters:

nobs (Optional[float]) – Weighted number of observations.
suff_stat (Tuple[int, np.ndarray, np.ndarray, np.ndarray]) – Sufficient statistics for dirichlet distribution.

Return type:

PoissonDistribution

Returns:

SequenceEncodableProbabilityDistribution

PoissonSampler

class dml.stats.poisson.PoissonSampler(dist, seed=None)

PoissonSampler object used to draw samples from PoissonDistribution.

rng

RandomState with seed set for sampling.

Type:: RandomState

dist

PoissonDistribution to sample from.

Type:: GeometricDistribution

sample(size=None)

Generate iid samples from Poisson distribution.

Generates a single Poisson sample (int) if size is None, else a numpy array of integers of length size containing iid samples, from the Poisson distribution.

Parameters:: size (Optional[int]) – Number of iid samples to draw. If None, assumed to be 1.
Return type:: Union[int, Sequence[int]]
Returns:: If size is None, int, else size length numpy array of ints.