Fig. 14

Comparison of circular probability density functions of sine and beta density. A Beta density with parameters a = b = 3.3818, matches closely that of the sine function, used as a probability density function (PDF). Beta density with parameters a = b = 3 solid line, is matched by sine function y = 1.05 − 1.1 cos(2π x/1.1). B Cumulative distribution function (CDF) is shown for these densities together with the difference between the two CDFs multiplied by 100 to visualize the comparison of the two distributions. C For testing different vector strengths we use uniform distributions with pre-set vector strengths (ρ = 0.8, 0.5 and 0.08)