APPENDIX CSOME PROPERTIES OF THE GOMPERTZ AND WEIBULL DISTRIBUTIONS

Here, λ > 0 and θ are parameters of the Gompertz distribution, and α > 0 and γ > 0 are parameters of the Weibull distribution. The hazard and cumulative hazard functions of the Gompertz distribution are given by, respectively,

(C.1)images
(C.2)images

Then, the Gompertz survival function, c.d.f., and p.d.f. are, respectively,

(C.3)images
(C.4)images
(C.5)images

The hazard and cumulative hazard functions of the Weibull distribution are, respectively,

(C.6)images
(C.7)images

The Weibull survival function, c.d.f., and p.d.f. are, respectively,

(C.8)images
(C.9)images
(C.10)

The life expectancy ...

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