Table 1:
Estimates of a Gompertz model without frailty and modified DeMoivre hazard models with Gammadistributed frailty (D_{female} denotes a dummy variable for females)









Data 
Male and Female Mortality in Bulgaria, 1992–93 

Age 40–95 

Method 
Gompertz hazard, no frailty 
Modified DeMoivre hazard function with Gammadistributed relative frailty 

Model 0 
Model 1 
Model 2 
Model 3 
Model 4 

Specification for a = exp(a_{0} + a_{1}D_{female}) 

a_{0} (Constant) 
5.5713 
5.6350 
5.5686 
5.4365 
5.5249 

(0.0117)* 
(0.0110)* 
(0.0114)* 
(0.0129)* 
(0.0116)* 
a_{1} (Female) 
1.3205 
0.7302 
0.8385 
1.1086 
0.9163 

(0.0198)* 
(0.0100)* 
(0.0117)* 
(0.0182)* 
(0.0139)* 

Specification for b = b_{0} + b_{1}D_{female} 

b_{0} (Constant) 
0.0825 
0.0755 
0.0749 
0.0687 
0.0740 

(0.0004)* 
(0.0004)* 
(0.0004)* 
(0.0005)* 
(0.0005)* 
b_{1} (Female) 
0.0254 
– 
– 
0.0103 
– 

(0.0006)* 


(0.0004)* 


Specification for s^{2} = exp(g_{0} + g_{1}D_{female}) 

g_{0} (Constant) 
– 
0.6186 
0.4876 
0.7411 
0.0960 


(0.0239)* 
(0.0234)* 
(0.0263)* 
(0.0281)* 
g_{1} (Female) 
– 
– 
0.4285 
– 
– 



(0.0255)* 



Specification for w 

w 
– 
set to 122.45 
set to 122.45 
set to 122.45 
104.2420 (0.3475)* 

Notes:
Standard errors in parentheses. pvalues: ^{+} p < 0.01; * p < 0.001.
Age has been rescaled in the estimation so that the parameter a reflects the mortality level of
the population at age 40, and s^{2} indicates the variance
of unobserved frailty at this age.
