Geometric¶

class paddle.distribution. Geometric ( probs ) [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 ) probs¶: Probability density/mass function.

Note

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

property mean: Mean of geometric distribution.

property variance: Variance of geometric distribution.

property stddev: Standard deviation of Geometric distribution.

pmf ( k ) 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 ) 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=() ) sample¶

Sample from Geometric distribution with sample shape.

Parameters: shape (tuple(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=() ) rsample¶

Generate samples of the specified shape.

Parameters: shape (tuple(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 ( ) 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 ) 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)

            

kl_divergence ( other ) [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)

            

property batch_shape

Returns batch shape of distribution

Returns: batch shape
Return type: Sequence[int]

property event_shape

Returns event shape of distribution

Returns: event shape
Return type: Sequence[int]

log_prob ( value ) log_prob¶: Log probability density/mass function.

prob ( value ) prob¶

Probability density/mass function evaluated at value.

Parameters: value (Tensor) – value which will be evaluated

Geometric¶

probs¶

pmf¶

log_pmf¶

sample¶

rsample¶

entropy¶

cdf¶

kl_divergence¶

log_prob¶

prob¶