Published court statistics read through Little's law — morie_backlog

Courts publish cases received, cases pending and a mean time to disposition over disposed cases. Over a window of days days with received filings, the time-average number pending \(L\) and the filing rate \(\lambda\) fix the mean time a case spends in court, \(W = L/\lambda\) (Research.P16.little, read backwards as little_target). The published mean counts only the cases disposed, so it is a truncated mean that understates the truth when the pending cases are older (Research.P16Censoring.disposed_understates); ratio is how far. With the published shares of disposed cases by duration band and the bands' lower edges, the disposed mean is at least the share-weighted sum of the floors (Research.P16Censoring.band_floor_le_mean); an open top band leaves no upper bound (no_upper_bound).

Usage

morie_backlog_published(
  received,
  days,
  pending,
  mean_days,
  band_shares = NULL,
  band_floors = NULL
)

Arguments

received: Cases received in each window.
days: Length of each window in days.
pending: Time-average number of cases pending over each window (the mean of the published month-end counts, for a monthly series).
mean_days: Published mean days to disposition of the cases disposed in each window.
band_shares: Optional matrix (one row per window, one column per band) of the shares of disposed cases in each duration band.
band_floors: Lower edge of each band in days (the first is usually 0).

Value

A data frame with filing_rate (per day), implied_mean_days (\(L/\lambda\)), published_mean_days, ratio (implied over published), little_backlog (\(\lambda\) times the published mean, the backlog the published mean would imply), pending, band_floor_bound (when bands are given) and the theorems attribute.

Examples

# Ontario Court of Justice, criminal, April 2024: 21,265 received in 30 days, 148,904
# pending, 175 published mean days; disposed shares under 10, 10-15, 15-18, over 18 months
morie_backlog_published(21265, 30, 148904, 175,
                        band_shares = rbind(c(0.808, 0.105, 0.034, 0.053)),
                        band_floors = c(0, 304, 456, 548))
#>   filing_rate implied_mean_days published_mean_days    ratio little_backlog
#> 1    708.8333          210.0691                 175 1.200395       124045.8
#>   pending band_floor_bound
#> 1  148904           76.468