scipy.special.nrdtrisd#

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

Calculate standard deviation of normal distribution given other params.

Parameters:

mnscalar or ndarray: The mean of the normal distribution.
parray_like: CDF values, in range (0, 1].
xarray_like: Quantiles, i.e. the upper limit of integration.
outndarray, optional: Optional output array for the function results

Returns:

stdscalar or ndarray: Standard deviation.

See also

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

Notes

Array API Standard Support

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

See Support for the array API standard for more information.

Examples

nrdtrisd can be used to recover the standard deviation of a normal distribution if we know the CDF value p for a given quantile x and the mean mn. 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 nrdtrisd returns the original value for std.

>>> from scipy.special import nrdtrisd
>>> nrdtrisd(mean, p, x)
2.0000000000000004