Circular standard deviation of clock times in decimal hours

Computes the circular SD using the mean resultant length formula: sqrt(-2 * log(R_bar)) * 24 / (2*pi), where R_bar is the mean resultant length of the unit-circle representation of the times. Linear SD inflates when times straddle midnight; this measure is invariant to the wrap point (Fix 24 in the JRSV pipeline).

Usage

circ_sd_h(x)

Arguments

x

numeric. Decimal hours in [0, 24). NA values are silently dropped. Returns NA_real_ for fewer than 2 values.

Value

A single non-negative numeric (hours), or NA_real_.

References

Mardia, K. V., & Jupp, P. E. (2000). Directional Statistics (2nd ed.). Wiley.

Examples

circ_sd_h(c(23.5, 0.5))   # small SD for times close to midnight
#> [1] 0.5007167
circ_sd_h(c(6.0, 18.0))   # large SD for times 12 h apart
#> [1] 33.00549