Modelling Deceleration in Senescent Mortality

Figures & data

FIGURE 1 Examples of accelerating and decelerating forces of mortality.

TABLE 1 Mortality Rate of Decrement (MRD)

Distribution	Force of mortality μ	MRD
Gompertz	αe ^βx	(1/β)ln 2
Weibull (γ > 1)	γβ(βx)^γ−1	(2^1/(γ−1))x
Linear	λ1 + λ2 x	λ1/λ2 + x

FIGURE 2 Shapes of distribution Eq. (32), with a = 0, c = d = 1.

FIGURE 3 Fit to Swedish death rates of various forces of mortality. Eq. (2-4) are almost overlying.

TABLE 2 Estimated Parameters for Swedish Mortality Data

Distribution	Parameters
μΓ	a = 0.018, b = 5.01, c = 2.5 × 10^5, d = 2.29
Weibull	γ = 0.014, β = 5.48
Lognormal	μ = 4.39, σ = 0.077
Logistic frailty	s = 0.569, A = 4.3 × 10^−7, α = 0.157
Logistic	γ = 0.011, k = 0.465, A = 1.9 × 10^−7, α = 0.174
Logistic Gompertz	k = 6.2 × 10^−4, A = 7.2 × 10^−4, B = 9.2 × 10^−7, α = 0.156

FIGURE 4 Velocity of μ_Γ (top panel) and its acceleration (bottom panel).

FIGURE 5 Fit to Medfly Data of Various Forces of Mortality. Eq. (2-4) are overlying.

TABLE 3 Estimated Parameters for Medfly Mortality Data

Distribution	Parameters
μΓ	a = 0.003, b = 5.01, c = 36.0, d = 0.425
Weibull	γ = 0.043, β = 2.36
Lognormal	μ = 2.93, σ = 0.484
Logistic frailty	s = 1.536, A = 0.002, α = 0.299
Logistic	γ = 5.4 × 10^−15, k = 0.127, A = 0.013, α = 0.299
Logistic Gompertz	k = 1.9 × 10^−67, A = 8.6 × 10^63, B = 0.013, α = 0.299

FIGURE 6 Velocity of μ_Γ (top panel) and its acceleration (bottom panel).