Exponential

Data Type: float

The exponential distribution is can be used to model arrival times between events. The distribution has support on the positive real line. The probability density function is given by

\[f\left(x | \beta \right) = \frac{1}{\beta}e^{-\frac{1}{\beta}x}, \; x \geq 0.\]

The above is the scale parametarization of the exponential distribution. For more info see Exponential Distribution.

ExponentialDistribution

class pysp.stats.exponential.ExponentialDistribution(beta, name=None, keys=None)

Exponential distribution with scale parameter beta.

beta

Positive real number defining the scale of the exponential distribution.

Type:: float

log_beta

Logarithm of the beta parameter.

Type:: float

name

Name for the ExponentialDistribution object.

Type:: Optional[str]

keys

Key for parameters.

Type:: Optional[str]

__init__(beta, name=None, keys=None)

Initialize ExponentialDistribution.

Parameters:

beta (float) – Positive real number defining the scale of the exponential distribution.
name (Optional[str], optional) – Name for the ExponentialDistribution object.
keys (Optional[str], optional) – Key for parameters.

density(x)

Evaluate the density of the exponential distribution at x.

Parameters:: x (float) – Positive real-valued number.
Returns:: Density evaluated at x.
Return type:: float

dist_to_encoder()

Return an ExponentialDataEncoder for this distribution.

Returns:: Encoder object.
Return type:: ExponentialDataEncoder

estimator(pseudo_count=None)

Return an ExponentialEstimator for this distribution.

Parameters:: pseudo_count (Optional[float], optional) – Pseudo-count for regularization.
Returns:: Estimator object.
Return type:: ExponentialEstimator

log_density(x)

Evaluate the log-density of the exponential distribution at x.

Parameters:: x (float) – Positive real-valued number.
Returns:: Log-density evaluated at x.
Return type:: float

sampler(seed=None)

Return an ExponentialSampler for this distribution.

Parameters:: seed (Optional[int], optional) – Seed for random number generator.
Returns:: Sampler object.
Return type:: ExponentialSampler

seq_log_density(x)

Vectorized log-density for encoded data.

Parameters:: x (ExponentialEncodedDataSequence) – Encoded data sequence.
Returns:: Log-density values.
Return type:: np.ndarray

ExponentialEstimator

class pysp.stats.exponential.ExponentialEstimator(pseudo_count=None, suff_stat=None, name=None, keys=None)

Estimator for the exponential distribution from aggregated sufficient statistics.

pseudo_count

Used to weight sufficient statistics.

Type:: Optional[float]

suff_stat

Positive float value for scale of exponential distribution.

Type:: Optional[float]

name

Name for the estimator.

Type:: Optional[str]

keys

Key for combining sufficient statistics.

Type:: Optional[str]

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

Initialize ExponentialEstimator.

Parameters:

pseudo_count (Optional[float], optional) – Used to weight sufficient statistics.
suff_stat (Optional[float], optional) – Positive float value for scale of exponential distribution.
name (Optional[str], optional) – Name for the estimator.
keys (Optional[str], optional) – Key for combining sufficient statistics.

Raises:

TypeError – If keys is not a string or None.

accumulator_factory()

Return an ExponentialAccumulatorFactory for this estimator.

Returns:: Factory object.
Return type:: ExponentialAccumulatorFactory

estimate(nobs, suff_stat)

Estimate an ExponentialDistribution from sufficient statistics.

Parameters:

nobs (Optional[float]) – Number of observations (not used).
suff_stat (Tuple[float, float]) – (count, sum) sufficient statistics.

Returns:

Estimated distribution.

Return type:

ExponentialDistribution

ExponentialSampler

class pysp.stats.exponential.ExponentialSampler(dist, seed=None)

Sampler for the exponential distribution.

dist

ExponentialDistribution instance to sample from.

Type:: ExponentialDistribution

rng

Random number generator.

Type:: RandomState

sample(size=None)

Draw iid samples from the exponential distribution.

Parameters:: size (Optional[int], optional) – Number of samples to draw. If None, returns a single sample.
Returns:: Single sample or array of samples.
Return type:: Union[float, np.ndarray]