A two-parameter hazard function to describe age patterns of mortality in ancient Northwestern Europe

Genus

Journal of Population Sciences

Table 6 Comparison of the mean fit to four models

	Mean weighted root mean square error
Dataset	2-Par. model^a	4-Par. model^b	Siler model^c	Brass ref level 12^d	Brass, best level per period (level)^e
Per period
EM 1640–1699 (n = 6)	0.174	0.162	0.191	0.200	0.178 (15)
EM 1700–1749 (n = 5)	0.187	0.162	0.170	0.185	0.184 (13)
EM 1750–1809 (n = 6)	0.158	0.147	0.163	0.166	0.165 (11)
HMD 1751–1800 (n = 50)	0.195	0.103	0.113	0.199	0.181 (8)
HMD 1801–1850 (n = 127)	0.111	0.071	0.077	0.135	0.132 (10)
HMD 1851–1900 (n = 350)	0.102	0.060	0.063	0.141	0.131 (7)
HMD 1901–1950 (n = 345)	0.066	0.036	0.049	0.120	0.103 (16)
HMD 1951–2000 (n = 350)	0.062	0.026	0.021	0.236	0.070 (24)
HMD 2001–2015 (n = 98)	0.105	0.040	0.029	0.284	0.086 (24)
Per country
HMD Belgium	0.0763	0.0403	0.0393	0.1621
HMD Denmark	0.0782	0.0420	0.0353	0.1799
EM England	0.1722	0.1567	0.1749	0.1835
HMD England & Wales	0.0726	0.0399	0.0495	0.1875
HMD France	0.1045	0.0582	0.0714	0.1784
HMD Netherlands	0.0812	0.0356	0.0351	0.1679
HMD Norway	0.0810	0.0448	0.0465	0.1778
HMD Sweden	0.1019	0.0537	0.0578	0.1613
All 1337 life tables	0.0877	0.0473	0.0506	0.1730

Notes:
^aOur two-parameter model: see equations 11a-c.
^bOur four-parameter model: see equations 2-5.
^cThe Siler model: see equation 1.
^dThe Brass logit method with Princeton Model West level 12 as its reference.
^eThe Brass logit method with the best-suited Princeton Model West level per period, taken from Additional file 1.
Source data: Human Mortality Database (2017, 2017, 2018); Wrigley et al. (1997: 224, 239, 250, 290)