Crimes prevented by a sentence of s periods served from career age
t0, when the offending rate falls with career age and a share r of
the crimes prevented is committed by someone else instead. The count is
at most s times the rate at the start of the sentence and at least s
times the rate at its end; the same sentence served one period later
prevents no more; and, net of replacement, the estimate from the rate at
the start is still an upper bound. The usual constant-rate estimate
therefore overstates what a sentence buys under both assumptions. See
proof("incapr").
Arguments
- lam
Offending rates by career age,
lam[1]at age 0: non-negative numbers that never increase.- t0
The career age at which the sentence starts: a whole number from 0, with
t0 + sat mostlength(lam) - 1.- s
The sentence in periods: a whole number from 1.
- r
The replacement share: one number from 0 to 1.
Value
A named numeric vector: prev (crimes prevented), net (net of
replacement), upper (s * lam at age t0), lower (s * lam at age
t0 + s) and later (crimes prevented by the same sentence from age
t0 + 1).
References
Shinnar, S. and Shinnar, R. (1975). The effects of the criminal justice system on the control of crime: a quantitative approach. Law and Society Review, 9(4), 581-611. doi:10.2307/3053340
Examples
incapr(lam = c(12, 10, 8, 6, 5, 4, 3, 2, 2, 1), t0 = 2, s = 3, r = 0.25)
#> prev net upper lower later
#> 19.00 14.25 24.00 12.00 15.00