gamma

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gamma#

class brainstate.random.gamma(shape, scale=None, size=None, key=None, dtype=None)#

Draw samples from a Gamma distribution.

Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale (sometimes designated “theta”), where both parameters are > 0.

Parameters:

  • shape (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – The shape of the gamma distribution. Must be non-negative.

  • scale (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – The scale of the gamma distribution. Must be non-negative. Default is equal to 1.

  • size (int | Sequence[int] | integer | Sequence[integer] | None) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if shape and scale are both scalars. Otherwise, np.broadcast(shape, scale).size samples are drawn.

  • key (int | Array | ndarray | None) – The key for the random number generator. If not given, the default random number generator is used.

Returns:

out – Drawn samples from the parameterized gamma distribution.

Return type:

Array | Quantity

Notes

The probability density for the Gamma distribution is

\[p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},\]

where \(k\) is the shape and \(\theta\) the scale, and \(\Gamma\) is the Gamma function.

The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.

References

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