Circular summaries and von Mises maximum likelihood (circular package conventions)

CircularSummary: mean direction, mean resultant length, circular variance and standard deviation, Rayleigh test p-value with the small-sample correction (Mardia and Jupp 2000). VonmisesMle: mean direction and concentration by the Best and Fisher (1981) inverse of \(A_1\), optional bias correction, standard errors and log-likelihood, as circular::mle.vonmises.

Usage

CircularSummary(theta)

VonmisesMle(theta, bias = FALSE)

Arguments

theta: Angles (radians).
bias: Apply the small-sample bias correction.

Value

List.

References

Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics. Wiley.

Best, D. J. and Fisher, N. I. (1981). The bias of the maximum likelihood estimators of the von Mises-Fisher concentration parameters. Communications in Statistics - Simulation and Computation 10, 493-502.

Examples

CircularSummary(c(0.1, 0.3, 6.2))$rbar
#> [1] 0.9877937
VonmisesMle(c(0.1, 0.3, 6.2, 0.05))$kappa
#> [1] 53.20097