scipy.special.pdtrik#

scipy.special.pdtrik(p, m, out=None) = <wrapped_ufunc 'pdtrik'>#

Inverse of pdtr with respect to k.

Parameters:

parray_like: Probability
marray_like: Shape parameter (nonnegative, real)
outndarray, optional: Optional output array for the function results

Returns:

scalar or ndarray: The number of occurrences k such that pdtr(k, m) = p

See also

pdtr: Poisson cumulative distribution function
pdtrc: Poisson survival function
pdtri: inverse of pdtr with respect to m

Notes

This function relies on the gamma_q_inva function from the Boost Math C++ library [1].

Array API Standard Support

pdtrik has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	✅	⛔
JAX	✅	⛔
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but typically none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. pdtrik does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

>>> import scipy.special as sc

Compute the CDF for several values of k:

>>> k = [1, 2, 3]
>>> p = sc.pdtr(k, 2)
>>> p
array([0.40600585, 0.67667642, 0.85712346])

Compute the inverse. We recover the values of k, as expected:

>>> sc.pdtrik(p, 2)
array([1., 2., 3.])