pypomp.random.poissoninv

pypomp.random.poissoninv(u: Array, lam: Array, dtype: dtype | None = None, max_newton_loops: int = 5, max_inverse_cdf_loops: int = 20) → Array[source]

Compute the approximate inverse Poisson CDF using JAX primitives.

Vectorised implementation of the inverse CDF for the Poisson distribution from Giles (2016) [1].

Parameters:

  • u (jax.Array) – Uniform probabilities in [0, 1]. Scalar or array.

  • lam (jax.Array) – Poisson rate parameter(s). Must be positive. Broadcast- compatible with u.

  • dtype (np.dtype or None, optional) – Floating-point dtype for intermediate computations and the return value. Inferred from inputs if None.

  • max_newton_loops (int, optional) – Maximum Newton-Raphson iterations. Defaults to 5.

  • max_inverse_cdf_loops (int, optional) – Maximum exact inverse CDF iterations. Defaults to 20.

Returns:

Array of Poisson quantiles with the broadcast shape of u and lam.

Return type:

jax.Array

Notes

For speed and accuracy metrics, see the Quant Tests.

See also

fast_poisson

High-level sampler that wraps this function.

References