Hướng dẫn chi-square cdf python

A chi-squared continuous random variable.

For the noncentral chi-square distribution, see ncx2.

As an instance of the rv_continuous class, chi2 object inherits from it a collection of generic methods [see below for the full list], and completes them with details specific for this particular distribution.

Notes

The probability density function for chi2 is:

\[f[x, k] = \frac{1}{2^{k/2} \Gamma \left[ k/2 \right]} x^{k/2-1} \exp \left[ -x/2 \right]\]

for \[x > 0\] and \[k > 0\] [degrees of freedom, denoted df in the implementation].

chi2 takes df as a shape parameter.

The chi-squared distribution is a special case of the gamma distribution, with gamma parameters a = df/2, loc = 0 and scale = 2.

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, chi2.pdf[x, df, loc, scale] is identically equivalent to chi2.pdf[y, df] / scale with y = [x - loc] / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.

Examples

>>> from scipy.stats import chi2 >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots[1, 1]

Calculate the first four moments:

>>> df = 55 >>> mean, var, skew, kurt = chi2.stats[df, moments='mvsk']

Display the probability density function [pdf]:

>>> x = np.linspace[chi2.ppf[0.01, df], ... chi2.ppf[0.99, df], 100] >>> ax.plot[x, chi2.pdf[x, df], ... 'r-', lw=5, alpha=0.6, label='chi2 pdf']

Alternatively, the distribution object can be called [as a function] to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pdf:

>>> rv = chi2[df] >>> ax.plot[x, rv.pdf[x], 'k-', lw=2, label='frozen pdf']

Check accuracy of cdf and ppf:

>>> vals = chi2.ppf[[0.001, 0.5, 0.999], df] >>> np.allclose[[0.001, 0.5, 0.999], chi2.cdf[vals, df]] True

Generate random numbers:

>>> r = chi2.rvs[df, size=1000]

And compare the histogram:

>>> ax.hist[r, density=True, histtype='stepfilled', alpha=0.2] >>> ax.legend[loc='best', frameon=False] >>> plt.show[]

Methods