pypomp.random.fast_binomial

pypomp.random.fast_binomial(key: Array, n: Array, p: Array, order: int = 2, exact_max: int = 5, dtype: dtype | None = None) → Array[source]

Sample binomial random variates using a GPU-optimized inverse CDF algorithm.

Generates binomial counts with parameters (n, p) using an approximate inverse incomplete beta function method. The implementation follows Giles and Beentjes (2024) [1], with an optional exact inverse CDF correction for small or extreme quantiles. Results are very close to exact but not guaranteed to be identical to a reference sampler.

Parameters:

  • key (jax.Array) – JAX PRNG key.

  • n (jax.Array) – Number of Bernoulli trials.

  • p (jax.Array) – Success probability in [0, 1].

  • order (int, optional) – Order of the beta-function approximation (0, 1, or 2). Defaults to 2 (most accurate).

  • exact_max (int, optional) – Maximum iterations for the bottom-up exact inverse CDF stage. Defaults to 5.

  • dtype (np.dtype or None, optional) – Output dtype (float or integer). Defaults to float64 if jax_enable_x64=True, otherwise float32. Integer dtypes return -1 for invalid inputs.

Returns:

Binomial samples with the broadcast shape of n and p and the specified dtype.

Return type:

jax.Array

Notes

For speed and accuracy metrics, see the Quant Tests.

Examples

>>> import jax
>>> import jax.numpy as jnp
>>> from pypomp.random import fast_binomial
>>> fast_binomial(jax.random.key(0), n=jnp.array(10), p=jnp.array(0.3))
Array(3., dtype=float32)

References