Detection-rate arithmetic of downgrade-and-caution — morie_detection_rate

Moving a share q of an offence class of size n with detection rate d into a disposal detected with probability one raises the aggregate detection rate by exactly \(q n (1 - d) / N\) while the recorded total \(N\) is unchanged (Research.P9.detection_rate_rises). An aggregate clearance rate therefore cannot serve as a performance signal without the split by disposal type.

Usage

morie_detection_rate_shift(detected, total, n, d, q)

Arguments

detected: Aggregate detections before the move.
total: Recorded total \(N\).
n: Size of the class being moved.
d: Detection rate of that class before the move, in [0, 1).
q: Share of the class moved, in (0, 1].

Value

A list with rate_before, rate_after, rise and theorem.

Examples

morie_detection_rate_shift(detected = 2000, total = 10000, n = 1500, d = 0.2, q = 0.5)
#> $rate_before
#> [1] 0.2
#> 
#> $rate_after
#> [1] 0.26
#> 
#> $rise
#> [1] 0.06
#> 
#> $theorem
#> [1] "Research.P9.detection_rate_rises"
#>