scipy.special.nrdtrimn#

scipy.special.nrdtrimn(p, std, x, out=None) = <wrapped_ufunc 'nrdtrimn'>#

Calculate mean of normal distribution given other params.

Parameters:

parray_like: CDF values, in range (0, 1].
stdarray_like: Standard deviation.
xarray_like: Quantiles, i.e. the upper limit of integration.
outndarray, optional: Optional output array for the function results

Returns:

mnscalar or ndarray: The mean of the normal distribution.

See also

scipy.stats.norm: Normal distribution
ndtr: Standard normal cumulative probability distribution
ndtri: Inverse of standard normal CDF with respect to quantile
nrdtrisd: Inverse of normal distribution CDF with respect to standard deviation

Notes

Array API Standard Support

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

See Support for the array API standard for more information.

Examples

nrdtrimn can be used to recover the mean of a normal distribution if we know the CDF value p for a given quantile x and the standard deviation std. First, we calculate the normal distribution CDF for an exemplary parameter set.

>>> from scipy.stats import norm
>>> mean = 3.
>>> std = 2.
>>> x = 6.
>>> p = norm.cdf(x, loc=mean, scale=std)
>>> p
0.9331927987311419

Verify that nrdtrimn returns the original value for mean.

>>> from scipy.special import nrdtrimn
>>> nrdtrimn(p, std, x)
3.0000000000000004