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📅 最后修改于: 2023-12-03 15:20:00.197000 🧑 作者: Mango
Scipy Stats.chi() | Python
The scipy.stats.chi() function calculates the probability density function (PDF) and cumulative distribution function (CDF) for the chi distribution. The chi distribution is a continuous probability distribution that arises in statistics and engineering for various applications, such as testing the goodness of fit of data, analyzing the time between random events, and estimating population variances.
Syntax
scipy.stats.chi(df, loc=0, scale=1)
df: degrees of freedomloc: location parameter (default is 0)scale: scale parameter (default is 1)
Parameters
x: array_like Values at which to evaluate the PDF or CDFdf: float or array_like Degrees of freedomloc: float or array_like Location parameter (default is 0)scale: float or array_like Scale parameter (default is 1)
Returns
pdf: ndarray or float Probability density function evaluated at xcdf: ndarray or float Cumulative distribution function evaluated at x
Examples
Probability Density Function (PDF)
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import chi
df = 3
fig, ax = plt.subplots(1, 1)
x = np.linspace(chi.ppf(0.01, df), chi.ppf(0.99, df), 100)
ax.plot(x, chi.pdf(x, df), 'r-', lw=5, alpha=0.6, label='chi pdf')
plt.legend(loc='best')
plt.show()
Cumulative Distribution Function (CDF)
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import chi
df = 3
fig, ax = plt.subplots(1, 1)
x = np.linspace(chi.ppf(0.01, df), chi.ppf(0.99, df), 100)
ax.plot(x, chi.cdf(x, df), 'b-', lw=5, alpha=0.6, label='chi cdf')
plt.legend(loc='best')
plt.show()
Random Variates
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import chi
df = 3
fig, ax = plt.subplots(1, 1)
r = chi.rvs(df, size=1000)
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
Conclusion
In conclusion, the scipy.stats.chi() function is useful for calculating the PDF and CDF of the chi distribution. The degree of freedom, location, and scale parameters can be adjusted to fit specific needs. The function can be used to test the goodness of fit of data, analyze time between random events, and estimate population variances.