Understanding the Von Mises quantile function + 95% CI?

Given the following ts:

ts <- c("08:43:48", "09:17:52", "12:56:22", "12:27:32", "10:59:23",
"07:22:45", "11:13:59", "10:13:26", "10:07:01", "06:09:56", "12:43:17",
"07:07:35", "09:36:44", "10:45:00", "08:27:36", "07:55:35", "11:32:56",
"13:18:35", "11:09:51", "09:46:33", "06:59:12", "10:19:36", "09:39:47",
"09:39:46", "18:23:54")


Converting to circular:

ts <- circular(ts, units = "hours", template = "clock24")

# Estimate the periodic mean from the von Mises distribution

estimates <- mle.vonmises(ts)

p_mean <- estimates$$mu %% 24 concentration <- estimates$$kappa

# Estimate densities of all 25 timestamps
densities <- dvonmises(ts, mu = p_mean, kappa = concentration)


Here is what I can't figure out, given alpha = 95%:

If I need a 95% CI why I need to tell qvonmises to calculate the percentile of (1-alpha)/2 - one number only. I have 2 tails clockwise and anti clockwise. Please clarify what I am missing here. Is it because this distribution is circular?

# Check if the densities are larger than the cutoff of 95%-CI
cutoff <- dvonmises(qvonmises((1 - alpha)/2, mu = p_mean, kappa = concentration), mu = p_mean, kappa = concentration)

# Define the variable time_feature
time_feature <- densities >= cutoff

• even after loading the circular package, your estimates <- mle.vonmises(ts) is giving me: Error in x/12 : non-numeric argument to binary operator – Henry Jan 20 at 19:42