scipy.special.pdtri#

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

Inverse to pdtr vs 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 gammaincinv(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) = p

See also

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

Notes

pdtri has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

>>> import scipy.special as sc

Compute the CDF for several values of m:

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

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

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