scipy.special.pdtri#

scipy.special.pdtri(k, y, out=None) = <ufunc 'pdtri'>#

Inverse of pdtr with respect to m.

Returns the Poisson variable m such that the sum from 0 to k of the Poisson density is equal to the given probability y: calculated by gammainccinv(k + 1, y). k must be a nonnegative integer and y between 0 and 1.

Parameters:

karray_like: Number of occurrences (nonnegative, real).
yarray_like: Probability.
outndarray, optional: Optional output array for the function results.

Returns:

scalar or ndarray: Values of the shape parameter m such that pdtr(k, m) = y.

See also

pdtr: Poisson cumulative distribution function
pdtrc: Poisson survival function
pdtrik: Inverse of pdtr with respect to k

Notes

Array API Standard Support

pdtri 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 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. pdtri does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

Examples

>>> import scipy.special as sc

Compute the CDF for several values of m:

>>> k = 1
>>> m = [0.5, 1, 1.5]
>>> p = sc.pdtr(k, m)
>>> p
array([0.90979599, 0.73575888, 0.5578254 ])

Invert the CDF with respect to the Poisson mean. We recover the values of m, as expected:

>>> sc.pdtri(k, p)
array([0.5, 1. , 1.5])

Verify the relation with gammainccinv:

>>> sc.gammainccinv(k + 1, p)
array([0.5, 1. , 1.5])