The decay of the chance of offending with distance from an offender's
base, in the forms of Brantingham and Brantingham (1981), Rossmo (2000)
and Levine (2009): "linear", f = max(0, A + B d), par = c(A, B);
"negexp", f = A exp(-b d), par = c(A, b) with b >= 0;
"normal", f = A dnorm(d, mu, s), par = c(A, mu, s); "lognormal",
f = A dlnorm(d, mu, s), par = c(A, mu, s) (the lognormal density of
d; some texts use log d^2 and 1 / d^2, which is not a density);
"trunc", the truncated negative exponential, f = P d / dp up to the
peak dp and P exp(-C (d - dp)) beyond, par = c(P, dp, C); and
"table", values tab at distances 0, delta, 2 delta, ..., linear in
between and 0 beyond, par = delta (as jtcal() tabulates).
References
Brantingham, P. J. and Brantingham, P. L. (1981). Environmental Criminology. Sage.
Levine, N. (2009). Introduction to the special issue on Bayesian journey-to-crime modelling. Journal of Investigative Psychology and Offender Profiling, 6(3), 167-185. doi:10.1002/jip.107