`scipy.stats._circstats:_circmeandev`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_circstats.py:13

Signature

def _circmeandev(sample, alpha, *, high = 6.283185307179586, low = 0)

Summary

Compute the circular mean (absolute) deviation of an angular sample.

Extended Summary

Given $n$ angle observations $x_{1}, \dots, x_{n}$ measured in radians, the circular mean (absolute) deviation about a given angle $α$ is defined by (^[1], Eq. 2.3.14)

d_{0} (α) = \frac{1}{n} i = 1 \sum n min (x_{i} - α, 2 π - (x_{i} - α)) .

For greater generality, this function computes:

d_{0} (α) = \frac{1}{n} i = 1 \sum n min (y_{i}, T - y_{i}),

where $y_{i} = (x_{i} - α) mod T$ and $T$ is the period of a full revolution (e.g. $360$ when working in degrees).

Parameters

sample : array_like: Input array of angle observations.
alpha : array_like: The reference angle with respect to which the mean deviation is computed.
high : float, optional: Upper boundary of the principal value of an angle. Default is 2*pi.
low : float, optional: Lower boundary of the principal value of an angle. Default is 0.

Returns

circmeandev : float: Circular mean (absolute) deviation, restricted to the range [low, high].

Examples

import numpy as np
from scipy.stats._circstats import _circmeandev
import matplotlib.pyplot as plt
sample = np.array([20, 30, 330])

✓

dev = _circmeandev(sample, sample, high=360, low=0)

✗

Among all the observations, the circular mean deviation is minimized about 20 degrees, so 20 degrees is the circular median.

Aliases

scipy.stats._circstats._circmeandev