`arkouda.scipy.stats`¶

Module Contents¶

Classes¶

chi2

A chi-squared continuous random variable.

class arkouda.scipy.stats.chi2(momtype=1, a=None, b=None, xtol=1e-14, badvalue=None, name=None, longname=None, shapes=None, seed=None)¶

Bases: scipy.stats._distn_infrastructure.rv_continuous

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.

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.

ncx2

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.
>>> import numpy as np
>>> 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, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

a(*args, **kwargs)¶: Convert a string or number to a floating point number, if possible.

b(*args, **kwargs)¶: Convert a string or number to a floating point number, if possible.

badvalue(*args, **kwargs)¶: Convert a string or number to a floating point number, if possible.

generic_moment(*args, **kwargs)¶

moment_type(*args, **kwargs)¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.__int__(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by ‘+’ or ‘-’ and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal. >>> int(‘0b100’, base=0) 4

name(*args, **kwargs)¶

str(object=’’) -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.__str__() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to ‘strict’.

numargs(*args, **kwargs)¶