scipy.stats.argus#
- scipy.stats.argus = <scipy.stats._continuous_distns.argus_gen object>[source]#
- Argus distribution - As an instance of the - rv_continuousclass,- argusobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- 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. - Notes - The probability density function for - argusis:\[f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2} \exp(-\chi^2 (1 - x^2)/2)\]- 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. - argustakes \(\chi\) as shape a parameter. Details about sampling from the ARGUS distribution can be found in [2].- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- argus.pdf(x, chi, loc, scale)is identically equivalent to- argus.pdf(y, chi) / scalewith- 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.- References [1]- “ARGUS distribution”, https://en.wikipedia.org/wiki/ARGUS_distribution [2]- Christoph Baumgarten “Random variate generation by fast numerical inversion in the varying parameter case.” Research in Statistics, vol. 1, 2023, doi:10.1080/27684520.2023.2279060. - Added in version 0.19.0. - Examples - >>> import numpy as np >>> from scipy.stats import argus >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> chi = 1 >>> lb, ub = argus.support(chi) - Calculate the first four moments: - >>> 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 - cdfand- ppf:- >>> 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, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim([x[0], x[-1]]) >>> ax.legend(loc='best', frameon=False) >>> plt.show() 