scipy.stats.chi2#
- scipy.stats.chi2 = <scipy.stats._continuous_distns.chi2_gen object>[source]#
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.See also
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
takesdf
as a shape parameter.The chi-squared distribution is a special case of the gamma distribution, with gamma parameters
a = df/2
,loc = 0
andscale = 2
.The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,chi2.pdf(x, df, loc, scale)
is identically equivalent tochi2.pdf(y, df) / scale
withy = (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
andppf
:>>> 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
rvs(df, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, df, loc=0, scale=1)
Probability density function.
logpdf(x, df, loc=0, scale=1)
Log of the probability density function.
cdf(x, df, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, df, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, df, loc=0, scale=1)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(x, df, loc=0, scale=1)
Log of the survival function.
ppf(q, df, loc=0, scale=1)
Percent point function (inverse of
cdf
— percentiles).isf(q, df, loc=0, scale=1)
Inverse survival function (inverse of
sf
).moment(order, df, loc=0, scale=1)
Non-central moment of the specified order.
stats(df, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(df, loc=0, scale=1)
(Differential) entropy of the RV.
fit(data)
Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.
expect(func, args=(df,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
Expected value of a function (of one argument) with respect to the distribution.
median(df, loc=0, scale=1)
Median of the distribution.
mean(df, loc=0, scale=1)
Mean of the distribution.
var(df, loc=0, scale=1)
Variance of the distribution.
std(df, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, df, loc=0, scale=1)
Confidence interval with equal areas around the median.