Geometric

class paddle.distribution. Geometric ( probs: float | Tensor ) [source]

Geometric distribution parameterized by probs.

In probability theory and statistics, the geometric distribution is one of discrete probability distributions, parameterized by one positive shape parameter, denoted by probs. In n Bernoulli trials, it takes k+1 trials to get the probability of success for the first time. In detail, it is: the probability that the first k times failed and the kth time succeeded. The geometric distribution is a special case of the Pascal distribution when r=1.

The probability mass function (pmf) is

$$Pr(Y=k)=(1-p)^kp$$

where k is number of trials failed before seeing a success, and p is probability of success for each trial and k=0,1,2,3,4…, p belong to (0,1].

Parameters :

probs (Real|Tensor) – Probability parameter. The value of probs must be positive. When the parameter is a tensor, probs is probability of success for each trial.

Returns :

Geometric distribution for instantiation of probs.

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> geom = Geometric(0.5)

>>> print(geom.mean)
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
1.)

>>> print(geom.variance)
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
2.)

>>> print(geom.stddev)
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
1.41421354)

probs ( value: Tensor ) → Tensor

probs¶

Probability density/mass function.

Note

This method will be deprecated in the future, please use prob instead.

property mean : Tensor

Mean of geometric distribution.

property variance : Tensor

Variance of geometric distribution.

property stddev : Tensor

Standard deviation of Geometric distribution.

pmf ( k: int | Tensor ) → Tensor

pmf¶

Probability mass function evaluated at k.

$$P(X=k) = (1-p)^{k} p, \quad k=0,1,2,3,\ldots$$

Parameters :

k (int) – Value to be evaluated.

Returns :

Probability.

Return type :

Tensor

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> geom = Geometric(0.5)
>>> print(geom.pmf(2))
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
0.12500000)

log_pmf ( k: int | Tensor ) → Tensor

log_pmf¶

Log probability mass function evaluated at k.

$$\log P(X = k) = \log(1-p)^k p$$

Parameters :

k (int) – Value to be evaluated.

Returns :

Log probability.

Return type :

Tensor

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> geom = Geometric(0.5)
>>> print(geom.log_pmf(2))
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
-2.07944131)

sample ( shape: Sequence[int] = [] ) → Tensor

sample¶

Sample from Geometric distribution with sample shape.

Parameters :

shape (Sequence[int]) – Sample shape.

Returns :

Sampled data with shape sample_shape + batch_shape + event_shape.

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> paddle.seed(2023)
>>> geom = Geometric(0.5)
>>> print(geom.sample((2,2)))
Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
[[0., 0.],
 [1., 0.]])

rsample ( shape: Sequence[int] = [] ) → Tensor

rsample¶

Generate samples of the specified shape.

Parameters :

shape (Sequence[int]) – The shape of generated samples.

Returns :

A sample tensor that fits the Geometric distribution.

Return type :

Tensor

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> paddle.seed(2023)
>>> geom = Geometric(0.5)
>>> print(geom.rsample((2,2)))
Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
[[0., 0.],
 [1., 0.]])

entropy ( ) → Tensor

entropy¶

Entropy of dirichlet distribution.

$$H(X) = -\left[\frac{1}{p} \log p + \frac{1-p}{p^2} \log (1-p) \right]$$

Returns :

Entropy.

Return type :

Tensor

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> geom = Geometric(0.5)
>>> print(geom.entropy())
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
1.38629425)

cdf ( k: int | Tensor ) → Tensor

cdf¶

Cdf of geometric distribution.

$$F(X \leq k) = 1 - (1-p)^(k+1), \quad k=0,1,2,\ldots$$

Parameters :

k – The number of trials performed.

Returns :

Entropy.

Return type :

Tensor

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> geom = Geometric(0.5)
>>> print(geom.cdf(4))
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
0.96875000)

property batch_shape : Sequence[int]

Returns batch shape of distribution

Returns :

batch shape

Return type :

Sequence[int]

property event_shape : Sequence[int]

Returns event shape of distribution

Returns :

event shape

Return type :

Sequence[int]

kl_divergence ( other: Geometric ) → Tensor [source]

kl_divergence¶

Calculate the KL divergence KL(self || other) with two Geometric instances.

$$KL(P \| Q) = \frac{p}{q} \log \frac{p}{q} + \log (1-p) - \log (1-q)$$

Parameters :

other (Geometric) – An instance of Geometric.

Returns :

The kl-divergence between two geometric distributions.

Return type :

Tensor

Examples

>>> import paddle
>>> from paddle.distribution import Geometric

>>> geom_p = Geometric(0.5)
>>> geom_q = Geometric(0.1)
>>> print(geom_p.kl_divergence(geom_q))
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
0.51082563)

log_prob ( value: Tensor ) → Tensor

log_prob¶

Log probability density/mass function.

prob ( value: Tensor ) → Tensor

prob¶

Probability density/mass function evaluated at value.

Parameters :

value (Tensor) – value which will be evaluated