Circular Statistics

Introduction

Working with circular data

Circular Data Description

Circular([low, upp, units, modulo, rad_low, ...]) Class to keep track of circular data
circ_axial(alpha[, m]) Transform p-axial data to a common scale (0, 2pi) in radians.
degrees Predefined instance of Circular for degrees in (0, 360)
clock24 Predefined instance of Circular for time or clock in (0, 24)
radshift Predefined instance of Circular for radians in (0, 2pi)

Basic Statistics

circ_resultant(alpha[, w, d, axis]) Compute mean resultant vector length for circular data
circ_mean(alpha[, w, return_ci, xi, axis]) Compute the mean direction for circular data.
circ_median(alpha[, axis]) Compute the median direction for circular data.
circ_var(alpha[, w, d, axis]) Compute circular variance for circular data (equ.
circ_std(alpha[, w, d, axis]) Compute circular standard deviation for circular data (equ.
circ_skewness(alpha[, w, axis]) Compute measures of angular skewness.
circ_kurtosis(alpha[, w, axis]) Compute measures of angular kurtosis.
circ_moment(alpha[, w, p, cent, axis]) Compute the complex p-th centered or non-centered circular moment.
circ_kappa(alpha[, w, method]) Estimate kappa of the von Mises distribution
circ_dist(x, y[, pairwise]) Compute pairwise distance, difference x_i-y_i, around the circle
circ_quantile(alpha, p[, mu]) quantiles of distribution centered at mu
circ_axialmean(alpha[, m, axis]) Compute the mean direction for circular data with axial correction.
circ_clust(alpha[, numclust, disp]) Perform a simple agglomerative clustering of angular data.
circ_corrcc(alpha1, alpha2) Circular correlation coefficient for two circular random variables.
circ_corrcl(alpha, x) Correlation coefficient between one circular and one linear random variable.

Inference

One Sample Tests

circ_medtest(alpha, md) One sample test for the median angle.
circ_mtest(alpha, mu0[, xi, w, d]) One sample test for the mean angle.
circ_symtest(alpha) Test for symmetry about the median.
circ_otest(alpha[, sz, w]) Omnibus or Hodges-Ajne test for uniform distribution of circular data.
circ_raotest(alpha) Rao’s spacing test for uniform distribution of circular data.
circ_rtest(alpha[, w, d, approx]) Rayleigh test for uniform distribution of circular data.
circ_vtest(alpha, mu0[, w, d]) V test for uniformity of circular data with a specified mean alternative.

Two and Multi Sample Tests

circ_cmtest(alpha, groups) Nonparametric multi-sample test for equal medians.
circ_hktest(alpha, idp, idq[, inter, fn]) Parametric two-way ANOVA for circular data with interations.
circ_ktest(alpha1, alpha2) A parametric two-sample test for equality of two concentration parameters.
circ_wwtest(alpha, groups[, w]) Parametric Watson-Williams multi-sample test for equal means.
circ_kuipertest(alpha1, alpha2[, res, vis_on]) Kuiper two-sample test for equality of distributions

Distributions

pdf_from_data(data[, k_comp]) get a pdf function for trigonometric series density
circ_pdf_from_moments(x, coeff_cos[, coeff_sin]) pdf evaluated at x for circular distribution given by moments
circ_cdf_from_moments(x, coeff_cos[, coeff_sin]) cdf evaluated at x for circular distribution given by moments
circ_moments_emp(x[, orders]) calculate circular moments for the data
circ_moments_from_pdf(pdf_func[, k_comp, ...]) calculate circular moments for a distribution given by its density
pdf_wrapcauchy(x, mean, a[, k_comp, neg]) pdf of wrapped cauchy distribution
cdf_wrapcauchy(x, mean, a[, k_comp]) cdf of wrapped cauchy distribution
coeffs_wrapcauchy(a, mu[, k_comp, neg]) coefficients for series expansion of wrapped cauchy distribution
pdf_wrapnormal(x, mean, var[, k_comp]) pdf of wrapped cauchy distribution
pdf_wrapstable(x, a, b, mu[, k_comp]) density of wrapped stable distribution
coeffs_wrapnormal(mean, var[, k_comp]) coefficients for series expansion of wrapped normal distribution
chf_cauchy(t, a, mu) characteristic function of cauchy distribution
chf_normal(t, mean, var) characteristic function of normal distribution
chf_stable(t, a, lambd, gamma, mu) characteristic function of stable distribution
pdf_wrapped_from_charfunc(chfunc[, args, k_comp]) returns a function that is the density of a wrapped distribution
cdf_wrapped_from_charfunc(chfunc[, args, k_comp]) returns a function that is the cumulative density of a wrapped distribution