scipy.stats.argus#
- scipy.stats.argus = <scipy.stats._continuous_distns.argus_gen object>[source]#
Argus distribution
As an instance of the
rv_continuous
class,argus
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
argus
is:\[f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2} \exp(-\chi^2 (1 - x^2)/2)\]for \(0 < x < 1\) and \(\chi > 0\), where
\[\Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2\]with \(\Phi\) and \(\phi\) being the CDF and PDF of a standard normal distribution, respectively.
argus
takes \(\chi\) as shape a parameter.The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,argus.pdf(x, chi, loc, scale)
is identically equivalent toargus.pdf(y, chi) / 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.References
- 1
“ARGUS distribution”, https://en.wikipedia.org/wiki/ARGUS_distribution
New in version 0.19.0.
Examples
>>> from scipy.stats import argus >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> chi = 1 >>> mean, var, skew, kurt = argus.stats(chi, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(argus.ppf(0.01, chi), ... argus.ppf(0.99, chi), 100) >>> ax.plot(x, argus.pdf(x, chi), ... 'r-', lw=5, alpha=0.6, label='argus 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 = argus(chi) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = argus.ppf([0.001, 0.5, 0.999], chi) >>> np.allclose([0.001, 0.5, 0.999], argus.cdf(vals, chi)) True
Generate random numbers:
>>> r = argus.rvs(chi, 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(chi, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, chi, loc=0, scale=1)
Probability density function.
logpdf(x, chi, loc=0, scale=1)
Log of the probability density function.
cdf(x, chi, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, chi, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, chi, loc=0, scale=1)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(x, chi, loc=0, scale=1)
Log of the survival function.
ppf(q, chi, loc=0, scale=1)
Percent point function (inverse of
cdf
— percentiles).isf(q, chi, loc=0, scale=1)
Inverse survival function (inverse of
sf
).moment(order, chi, loc=0, scale=1)
Non-central moment of the specified order.
stats(chi, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(chi, 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=(chi,), 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(chi, loc=0, scale=1)
Median of the distribution.
mean(chi, loc=0, scale=1)
Mean of the distribution.
var(chi, loc=0, scale=1)
Variance of the distribution.
std(chi, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, chi, loc=0, scale=1)
Confidence interval with equal areas around the median.