scipy.stats.vonmises_line#
- scipy.stats.vonmises_line = <scipy.stats._continuous_distns.vonmises_gen object>[source]#
- A Von Mises continuous random variable. - As an instance of the - rv_continuousclass,- vonmises_lineobject 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(kappa, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, kappa, loc=0, scale=1) - Probability density function. - logpdf(x, kappa, loc=0, scale=1) - Log of the probability density function. - cdf(x, kappa, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, kappa, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, kappa, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, kappa, loc=0, scale=1) - Log of the survival function. - ppf(q, kappa, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, kappa, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, kappa, loc=0, scale=1) - Non-central moment of the specified order. - stats(kappa, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(kappa, 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=(kappa,), 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(kappa, loc=0, scale=1) - Median of the distribution. - mean(kappa, loc=0, scale=1) - Mean of the distribution. - var(kappa, loc=0, scale=1) - Variance of the distribution. - std(kappa, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, kappa, loc=0, scale=1) - Confidence interval with equal areas around the median. - See also - scipy.stats.vonmises_fisher
- Von-Mises Fisher distribution on a hypersphere 
 - Notes - The probability density function for - vonmisesand- vonmises_lineis:\[f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) }\]- for \(-\pi \le x \le \pi\), \(\kappa \ge 0\). \(I_0\) is the modified Bessel function of order zero ( - scipy.special.i0).- vonmisesis a circular distribution which does not restrict the distribution to a fixed interval. Currently, there is no circular distribution framework in SciPy. The- cdfis implemented such that- cdf(x + 2*np.pi) == cdf(x) + 1.- vonmises_lineis the same distribution, defined on \([-\pi, \pi]\) on the real line. This is a regular (i.e. non-circular) distribution.- Note about distribution parameters: - vonmisesand- vonmises_linetake- kappaas a shape parameter (concentration) and- locas the location (circular mean). A- scaleparameter is accepted but does not have any effect.- Examples - Import the necessary modules. - >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.stats import vonmises - Define distribution parameters. - >>> loc = 0.5 * np.pi # circular mean >>> kappa = 1 # concentration - Compute the probability density at - x=0via the- pdfmethod.- >>> vonmises.pdf(0, loc=loc, kappa=kappa) 0.12570826359722018 - Verify that the percentile function - ppfinverts the cumulative distribution function- cdfup to floating point accuracy.- >>> x = 1 >>> cdf_value = vonmises.cdf(x, loc=loc, kappa=kappa) >>> ppf_value = vonmises.ppf(cdf_value, loc=loc, kappa=kappa) >>> x, cdf_value, ppf_value (1, 0.31489339900904967, 1.0000000000000004) - Draw 1000 random variates by calling the - rvsmethod.- >>> sample_size = 1000 >>> sample = vonmises(loc=loc, kappa=kappa).rvs(sample_size) - Plot the von Mises density on a Cartesian and polar grid to emphasize that it is a circular distribution. - >>> fig = plt.figure(figsize=(12, 6)) >>> left = plt.subplot(121) >>> right = plt.subplot(122, projection='polar') >>> x = np.linspace(-np.pi, np.pi, 500) >>> vonmises_pdf = vonmises.pdf(x, loc=loc, kappa=kappa) >>> ticks = [0, 0.15, 0.3] - The left image contains the Cartesian plot. - >>> left.plot(x, vonmises_pdf) >>> left.set_yticks(ticks) >>> number_of_bins = int(np.sqrt(sample_size)) >>> left.hist(sample, density=True, bins=number_of_bins) >>> left.set_title("Cartesian plot") >>> left.set_xlim(-np.pi, np.pi) >>> left.grid(True) - The right image contains the polar plot. - >>> right.plot(x, vonmises_pdf, label="PDF") >>> right.set_yticks(ticks) >>> right.hist(sample, density=True, bins=number_of_bins, ... label="Histogram") >>> right.set_title("Polar plot") >>> right.legend(bbox_to_anchor=(0.15, 1.06)) 