theilslopes(y, x=None, alpha=0.95, method='separate')
theilslopes implements a method for robust linear regression. It computes the slope as the median of all slopes between paired values.
The implementation of theilslopes follows . The intercept is not defined in , and here it is defined as median(y) - slope*median(x), which is given in . Other definitions of the intercept exist in the literature such as median(y - slope*x) in . The approach to compute the intercept can be determined by the parameter method. A confidence interval for the intercept is not given as this question is not addressed in .
For compatibility with older versions of SciPy, the return value acts like a namedtuple of length 4, with fields slope, intercept, low_slope, and high_slope, so one can continue to write
slope, intercept, low_slope, high_slope = theilslopes(y, x)
Dependent variable.
Independent variable. If None, use arange(len(y)) instead.
Confidence degree between 0 and 1. Default is 95% confidence. Note that alpha is symmetric around 0.5, i.e. both 0.1 and 0.9 are interpreted as "find the 90% confidence interval".
Method to be used for computing estimate for intercept. Following methods are supported,
- 'joint': Uses np.median(y - slope * x) as intercept.
The default is 'separate'.
The return value is an object with the following attributes:
slope
slope
intercept
intercept
low_slope
low_slope
high_slope
high_slope
Computes the Theil-Sen estimator for a set of points (x, y).
siegelslopes
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
x = np.linspace(-5, 5, num=150)
y = x + np.random.normal(size=x.size)
y[11:15] += 10 # add outliers
y[-5:] -= 7
res = stats.theilslopes(y, x, 0.90, method='separate')
lsq_res = stats.linregress(x, y)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, y, 'b.')
ax.plot(x, res[1] + res[0] * x, 'r-')
ax.plot(x, res[1] + res[2] * x, 'r--')
ax.plot(x, res[1] + res[3] * x, 'r--')
ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.stats._mstats_basic:theilslopes
scipy.stats._mstats_basic:sen_seasonal_slopes
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