Incident versus offence counting: the hierarchy-rule arithmetic

Under a hierarchy rule an incident with several offences is counted once (its most serious offence); an offence-based system counts every offence. With \(N\) incidents carrying \(k_i \ge 1\) offences each, bounded by \(K\), the offence count lies in \([N, KN]\) and equals \(N(1 + \bar{e})\) with \(\bar{e}\) the mean number of extra offences per incident (Research.P1.offence_count_bounds, offence_count_eq); the offence total is not a function of the incident total (category_not_identified). A switch from incident to offence counting therefore raises recorded crime with no change in crime, by exactly the mean extra offences per incident.

Usage

morie_dark_figure_hierarchy(offences_per_incident)

Arguments

offences_per_incident

Integer vector, one entry per incident, each at least 1.

Value

A list with incidents, offences, ratio (offences per incident), mean_extra, bounds (\([N, KN]\) with \(K\) the observed maximum) and theorems.

Examples

morie_dark_figure_hierarchy(c(1, 1, 2, 1, 3, 1, 1, 2))
#> $incidents
#> [1] 8
#> 
#> $offences
#> [1] 12
#> 
#> $ratio
#> [1] 1.5
#> 
#> $mean_extra
#> [1] 0.5
#> 
#> $bounds
#> lower upper 
#>     8    24 
#> 
#> $theorems
#> [1] "Research.P1.offence_count_bounds"    "Research.P1.offence_count_eq"       
#> [3] "Research.P1.category_not_identified"
#>