Feature Checklist

1. Descriptive Statistics

Feature	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Measures of Central Tendency
Circular Mean	`circ_mean`	`mean(alpha)`	`circ_mean(alpha)`	`circ.mean`	`mean.circular`
Circular Mean CI	`circ_mean_ci`	`mean(alpha, ci=95)`	`circ_confmean`	-	`mle.vonmises.bootstrap.ci`
Circular Median	`circ_median`	`median`	`circ_median`	-	`median.circular`/`medianHL.circular`
Circular Median CI	`circ_median_ci`	-	-	-	-
Circular Quantile	`circ_quantile`	-	-	-	`quantile.circular`
Measures of Spread & Dispersion
Resultant Vector Length	`circ_r`	`resultant_vector_length`	`circ_r`	`est.rho`	`rho.circular`
Angular Variance	`angular_var`	`avar`	`circ_var`	-	`angular.variance`
Angular Standard Deviation	`angular_std`	`astd`	`circ_std`	-	`angular.deviation`
Circular Variance	`circ_var`	`var`	`circ_var`	`circ.disp`	`var.circular`
Circular Standard Deviation	`circ_std`	`std`	`circ_std`	-	`sd.circular`
Circular Dispersion	`circ_dispersion`	-	-	-	-
Higher-Order Statistics
Circular Moment	`circ_moment`	`moment`	`circ_moment`	`tri.moment`	`trigonometric.moment`
Circular Skewness	`circ_skewness`	`skewness`	`circ_skewness`	-	-
Circular Kurtosis	`circ_kurtosis`	`kurtoisis`	`circ_kurtosis`	-	-
Distance & Pairwise Comparisons
Mean deviation	`circ_mean_deviation`	-	-	-	`meandeviation`
Circular Distance	`circ_dist`	`cdist`	`circ_dist`	-	-
Pairwise Circular Distance	`circ_pairdist`	`pairwise_cdiff`	`circ_dist2`	-	`dist.circular`

2. Hypothesis Testing

One-Sample Tests for Significance

Feature	H0	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Mean Direction
Rayleigh Test	\(\rho=0\) ¹	`rayleigh_test`	`rayleigh`	`circ_rtest`	`r.test`	`rayleigh.test`
V-Test	\(\rho=0\)	`V_test`	`vtest`	`circ_vtest`	`v0.test`	-
One-sample Test	\(\tilde\mu=μ_0\)	`one_sample_test`	`mtest`	`circ_mtest`	-	-
Change Point Test	no change point	`change_point_test`	-	-	`change.pt`	`change.point`
Median Direction
Hodges-Ajne (omnibus) Test	\(\rho=0\)	`omnibus_test`	`omnibus`	`circ_otest`	-	-
Batschelet Test	\(\rho=0\)	`batschelet_test`	-	-	-	-
Binomial Test	\(\tilde\theta = \theta_0\) ²	`binomial_test`	`medtest`	`circ_medtest`	-	-
Symmetry Test around median	\(\text{symmetry}\)	`symmetry_test`	`symtest`	`circ_symtest`	-	-

Multi-Sample Tests for Significance

Feature	H0	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Mean Direction
Circular Analysis of Variance	\(\mu_1 = \dots = \mu_n\)	`circ_anova`	-	-	-	`aov.circular`
Watson-Williams Test ⁴	\(\mu_1 = \dots = \mu_n\)	`watson_williams_test`	`watson_williams`	`circ_wwtest`	-	`watson.williams.test`
Harrison-Kanji Test⁵	\(\mu_1 = \dots = \mu_n\)	`harrison_kanji_test`	`hktest`	`circ_hktest`	-	-
Median Direction
Common Median Test	\(\tilde{\theta}_1 = \dots = \tilde{\theta}_n\)	`common_median_test`	`cmtest`	`circ_cmtest`	-	-
Concentration
Concentration Test (F-test)	\(\kappa_1 = \dots = \kappa_n\)	`concentration_test`	-	`circ_ktest`	-	-
Equal Kappa Test	\(\kappa_1 = \dots = \kappa_n\)	`equal_kappa_test`	-	-	-	`equal.kappa.test`
Distribution Homogeneity
Watson's U2 Test	\(F_1 = F_2\) ³	`watson_u2_test`	-	-	`watson.two`	`watson.two.test`
Wallraff Test	\(F_1 = F_2\)	`wallraff_test`	-	-	-	`wallraff.test`
Wheeler-Watson Test	\(F_1 = F_2\)	`wheeler_watson_test`	-	-	-	`watson.wheeler.test`
Angular Randomization Test	\(F_1 = F_2\)	`angular_randomisation_test`	-	-	-	-
Rao's Tests for Homogeneity	\(F_1 = F_2\)	`rao_homogeneity_test`	-	-	`rao.homogeneity`	`rao.test`

Goodness-of-fit Tests

Feature	H0	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Kuiper’s Test	\(\rho = 0\)	`circ_kuiper_test`	`kupier`	`circ_kuipertest`	`kuiper`	`kuiper.test`
Rao’s Spacing Test	\(\rho = 0\)	`rao_spacing_test`	`raospacing`	`circ_raotest`	`rao.spacing`	`rao.spacing.test`
Watson's Test	\(\rho = 0\)	`watson_test`	-	-	`watson`	`watson.test`
Circular Range Test	\(\rho = 0\)	`circ_range_test`	-	-	`circ_range`	`range.circular`

3. Correlation & Regression

Feature	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Circular-Circular Correlation	`circ_corrcc`	`corrcc`	`circ_corrcc`	`circ.cor`	`cor.circular`
Circular-Linear Correlation	`circ_corrcl`	`corrcl`	`circ_corrcl`	-	-
Circular-Circular Regression	`CCRegression`	-	-	`circ.reg`	`lm.circular(type="c-c")`
Circular-Linear Regression	`CLRegression`	-	-	-	`lm.circular(type="c-l")`

4. Circular Distributions

All circular distributions assume angles are on [0, 2π). Inputs are automatically wrapped to that support as a convenience. We remove SciPy's loc/scale convention—parameters like mu, rho, etc. are the only inputs.

Symmetric Circular Distributions

Feature	Method	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Circular Uniform	PDF	`circularuniform.pdf`	-	-	-	`dcircularuniform`
	CDF	`circularuniform.cdf`	-	-	-	-
	PPF	`circularuniform.ppf`	-	-	-	-
	RVS	`circularuniform.rvs`	-	-	-	`rcircularuniform`
	Fit	`circularuniform.fit`	-	-	-	-
Triangular	PDF	`triangular.pdf`	`triangular.pdf`	-	`dtri`	-
	CDF	`triangular.cdf`	`triangular.cdf`	-	-	-
	PPF	`triangular.ppf`	`triangular.ppf`	-	-	-
	RVS	`triangular.rvs`	`triangular.rvs`	-	`rtri`	-
	Fit	`triangular.fit`	`triangular.fit`	-	-	-
Cardioid	PDF	`cardioid.pdf`	`cardioid.pdf`	-	`dcard`	`dcardioid`
	CDF	`cardioid.cdf`	`cardioid.cdf`	-	-	-
	PPF	`cardioid.ppf`	`cardioid.ppf`		-	-
	RVS	`cardioid.rvs`	`cardioid.rvs`	-	`rcard`	`rcardioid`
	Fit	`cardioid.fit`	`cardioid.fit`	-	-
Cartwright	PDF	`cartwright.pdf`	-	-	-	`dcarthwrite`
	CDF	`cartwright.cdf`	-	-	-	-
	PPF	`cartwright.ppf`	-	-	-	-
	RVS	`cartwright.rvs`	-	-	-	-
	Fit	`cartwright.fit`	-	-	-	-
Wrapped Normal	PDF	`wrapnorm.pdf`	-	-	`dwrpnorm`	`dwrappednormal`
	CDF	`wrapnorm.cdf`	-	-	-	`pwrappednormal`
	PPF	`wrapnorm.ppf`	-	-	-	`qwrappednormal`
	RVS	`wrapnorm.rvs`	-	-	`rwrpnorm`	`rwrappednormal`
	Fit	`wrapnorm.fit`	-	-	-	`mle.wrappednormal`
Wrapped Cauchy	PDF	`wrapcauchy.pdf`	-	-	`dwrpcauchy`	`dwrappedcauchy`
	CDF	`wrapcauchy.cdf`	-	-	-	-
	PPF	`wrapcauchy.ppf`	-	-	-	-
	RVS	`wrapcauchy.rvs`	-	-	`rwrpcauchy`	`rwrappedcauchy`
	Fit	`wrapcauchy.fit`	-	-	-	`mle.wrappedcauchy`
Von Mises	PDF	`vonmises.pdf`	-	`circ_vmpdf`	`dvm`	`dvonmises`
	CDF	`vonmises.cdf`	-	-	`pvm`	`pvonmises`
	PPF	`vonmises.ppf`	-	-	-	`qvonmises`
	RVS	`vonmises.rvs`	-	`circ_vmrnd`	`rvm`	`rvonmises`
	Fit	`vonmises.fit`	-	`circ_vmpar`	`vm.ml`	`mle.vonmises`
Flattopped Von Mises	PDF	`vonmises_flattopped.pdf`	-	-	-	-
	CDF	`vonmises_flattopped.cdf`	-	-	-	-
	PPF	`vonmises_flattopped.ppf`	-	-	-	-
	RVS	`vonmises_flattopped.rvs`	-	-	-	-
	Fit	`vonmises_flattopped.fit`	-	-	-	-
Jones-Pewsey	PDF	`jonespewsey.pdf`	-	-	-	`djonespewsey`
	CDF	`jonespewsey.cdf`	-	-	-	-
	PPF	`jonespewsey.ppf`	-	-	-	-
	RVS	`jonespewsey.rvs`	-	-	-	-
	Fit	`jonespewsey.fit`	-	-	-	-

Asymmetric Circular Distributions

Feature	Method	PyCircStat2	PyCircStat	CircStat (MATLAB)	CircStats (R)	circular (R)
Jones-Pewsey Sine-Skewed	PDF	`jonespewsey_sineskewed.pdf`	-	-	-	-
	CDF	`jonespewsey_sineskewed.cdf`	-	-	-	-
	PPF	`jonespewsey_sineskewed.ppf`	-	-	-	-
	RVS	`jonespewsey_sineskewed.rvs`	-	-	-	-
	Fit	`jonespewsey_sineskewed.fit`	-	-	-	-
Jones-Pewsey Asymmetric	PDF	`jonespewsey_asym.pdf`	-	-	-	-
	CDF	`jonespewsey_asym.cdf`	-	-	-	-
	PPF	`jonespewsey_asym.ppf`	-	-	-	-
	RVS	`jonespewsey_asym.rvs`	-	-	-	-
	Fit	`jonespewsey_asym.fit`	-	-	-	-
Inverse Batschelet	PDF	`inverse_batschelet.pdf`	-	-	-	-
	CDF	`inverse_batschelet.cdf`	-	-	-	-
	PPF	`inverse_batschelet.ppf`	-	-	-	-
	RVS	`inverse_batschelet.rvs`	-	-	-	-
	Fit	`inverse_batschelet.fit`	-	-	-	-
Kato-Jones	PDF	`katojones.pdf`	-	-	-	`dkatojones`
	CDF	`katojones.cdf`	-	-	-	-
	PPF	`katojones.ppf`	-	-	-	-
	RVS	`katojones.rvs`	-	-	-	`rkatojones`
	Fit	`katojones.fit`	-	-	-	-
Wrapped Stable	PDF	`wrapstable.pdf`	-	-	-	-
	CDF	`wrapstable.cdf`	-	-	-	-
	PPF	`wrapstable.ppf`	-	-	-	-
	RVS	`wrapstable.rvs`	-	-	`rwrpstab`	-
	Fit	`wrapstable.fit`	-	-	-	-
Asymmetric Trangular	PDF	-	-	-	-	`dasytriangular`
Projected Normal	PDF	-	-	-	-	`dpnorm`
	RVS	-	-	-	-	`rpnorm`

\(\rho=0\) stands for uniform distributed. ↩
\(\theta\) stands for median. ↩
\(F\) stands for distributions. ↩
Yet anothr one-way ANOVA. ↩
Two-way ANOVA. ↩