Gamma

Data Type: float

The gamma distribution is a generalization of the exponential distribution. The distribution has support on the positive real line. The probability density function is given by

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

The above is the scale parametarization of the gamma distribution. For more info see Gamma Distribution.

GammaDistribution

class dmx.stats.gamma.GammaDistribution(k, theta, name=None, keys=None)

Gamma distribution with shape k and scale theta.

k

Positive real-valued shape parameter.

Type:: float

theta

Positive real-valued scale parameter.

Type:: float

name

Name for the GammaDistribution instance.

Type:: Optional[str]

log_const

Normalizing constant of gamma distribution.

Type:: float

keys

Key for parameters of distribution.

Type:: Optional[str]

__init__(k, theta, name=None, keys=None)

Initialize GammaDistribution.

Parameters:

k (float) – Positive real-valued shape parameter.
theta (float) – Positive real-valued scale parameter.
name (Optional[str], optional) – Name for the GammaDistribution instance.
keys (Optional[str], optional) – Key for parameters of distribution.

density(x)

Evaluate the density of the gamma distribution at x.

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

dist_to_encoder()

Return a GammaDataEncoder for this distribution.

Returns:: Encoder object.
Return type:: GammaDataEncoder

estimator(pseudo_count=None)

Return a GammaEstimator for this distribution.

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

log_density(x)

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

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

sampler(seed=None)

Return a GammaSampler for this distribution.

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

seq_log_density(x)

Vectorized log-density for encoded data.

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

GammaEstimator

class dmx.stats.gamma.GammaEstimator(pseudo_count=(0.0, 0.0), suff_stat=(1.0, 0.0), threshold=1e-08, name=None, keys=None)

Estimator for the gamma distribution from aggregated sufficient statistics.

pseudo_count

Values used to re-weight sufficient statistics.

Type:: Tuple[float, float]

suff_stat

Prior shape ‘k’ and scale ‘theta’.

Type:: Tuple[float, float]

threshold

Threshold for estimating the shape of gamma.

Type:: float

name

Name for the estimator.

Type:: Optional[str]

keys

Key for combining sufficient statistics.

Type:: Optional[str]

__init__(pseudo_count=(0.0, 0.0), suff_stat=(1.0, 0.0), threshold=1e-08, name=None, keys=None)

Initialize GammaEstimator.

Parameters:

pseudo_count (Tuple[float, float], optional) – Values used to re-weight sufficient statistics.
suff_stat (Tuple[float, float], optional) – Prior shape ‘k’ and scale ‘theta’.
threshold (float, optional) – Threshold for estimating the shape of gamma.
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 a GammaAccumulatorFactory for this estimator.

Returns:: Factory object.
Return type:: GammaAccumulatorFactory

estimate(nobs, suff_stat)

Estimate a GammaDistribution from sufficient statistics.

Parameters:

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

Returns:

Estimated distribution.

Return type:

GammaDistribution

static estimate_shape(avg_sum, avg_sum_of_logs, threshold)

Estimate the shape parameter of the GammaDistribution.

Parameters:

avg_sum (float) – Weighted mean of gamma observations.
avg_sum_of_logs (float) – Weighted mean of log gamma observations.
threshold (float) – Threshold for convergence of shape estimation.

Returns:

Estimate of shape parameter ‘k’.

Return type:

float

GammaSampler

class dmx.stats.gamma.GammaSampler(dist, seed=None)

Sampler for the gamma distribution.

rng

Random number generator.

Type:: RandomState

dist

GammaDistribution to sample from.

Type:: GammaDistribution

seed

Seed for random number generator.

Type:: Optional[int]

sample(size=None)

Draw iid samples from the gamma distribution.

Parameters:: size (Optional[int], optional) – Number of iid samples to draw. If None, returns a single sample.
Returns:: Single sample (float) if size is None, else a list of samples.
Return type:: Union[float, List[float]]