Beta

Beta distribution for binary data.

A Beta distribution is very similar to a Bernoulli distribution in that it counts occurrences of boolean events. The differences lies in what is being measured. A Binomial distribution models the probability of an event occurring, whereas a Beta distribution models the probability distribution itself. In other words, it's a probability distribution over probability distributions.

Parameters

• alpha

  Type → int

  Default → 1

  Initial alpha parameter.

• beta

  Type → int

  Default → 1

  Initial beta parameter.

• seed

  Type → int | None

  Default → None

  Random number generator seed for reproducibility.

Attributes

• mode

  The most likely value in the distribution.

• n_samples

  The number of observed samples.

Examples

from river import proba

successes = 81
failures = 219
beta = proba.Beta(successes, failures)

beta(.21), beta(.35)

(0.867..., 0.165...)

for success in range(100):
    beta = beta.update(True)
for failure in range(200):
    beta = beta.update(False)

beta(.21), beta(.35)

(2.525...e-05, 0.841...)

beta.cdf(.35)

0.994168...

Methods

call

Probability mass/density function.

Parameters

• p — 'float'

cdf

Cumulative density function, i.e. P(X <= x).

Parameters

• x — 'float'

revert

Reverts the parameters of the distribution for a given observation.

Parameters

• x — 'float'

sample

Sample a random value from the distribution.

update

Updates the parameters of the distribution given a new observation.

Parameters

• x — 'float'

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1. What is the intuition behind beta distribution? ↩