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Journal Article
Demography (1981) 18 (2): 231–244.
Published: 01 May 1981
... were a cubic spline, the Hadwiger and Coale-Trussell functions, the gamma and beta densities, two versions of a polynomial, and two of Brass's relational procedures, as well as the Gompertz curve. The spline function fitted all curves far better than any of the others. The Coale-Trussell procedure...
Journal Article
Demography (1969) 6 (2): 185–221.
Published: 01 May 1969
... the gamma density fa(Y) = e-uya-I/r{a) YI(t) I XI(t) has the gamma density with a = .2 XI(t); Y 2(t) I XI(t) has the gamma density with a = .3 XI(t); Y 3 (t) I XI(t) has the gamma density with a = .5 XI(t); Y,(t) I X 2{t) has the gamma density with a = .25 X 2 {t) ; Y 6 {t) I X 2 (t) has the gamma density...
Journal Article
Demography (1988) 25 (2): 277–287.
Published: 01 May 1988
... h(Xlz)/tz)g(zX) = <Xl 'fo h(Xlz)/tz) dz where h(Xlz) is given, as before, by equation (14). It is not difficult to show that g(zIX) is a gamma density function. The son's life expectancy conditional on his father's life span is given by (17) Inherited Frailty and Longevity 285 The curve...
Journal Article
Demography (1980) 17 (2): 207–223.
Published: 01 May 1980
... of the amenorrhea and the conception lead- ing to the live birth. It is assumed to have a gamma distribution. More specifically, define Amj = Am/ - 0.8 (j 2). We sup- pose that Am j is a realization from a gamma distribution with density f(x; !J.mj, k) ex: exp(-kx/!J.m) xk-l, x > O(j 2). Because of the uncertainty...
Journal Article
Demography (1990) 27 (2): 267–284.
Published: 01 May 1990
... normal density function and ~o = (In t - xP)/a; A( I ) _ a-I exp(-xp/a)ta-I - 1 t x - I + exp( -xp/a)ta-I-l' Iyl/at {[exp( - xP)tlyla/yZ}' /y2 exp{- [exp(- xp)tjYla/ yZ} A(t I x) = t5f(lIyZ) + (-I)<lr{lIyZ, [exp( _xp)tjYla/yZ} , where t5 = 1 if y < 0 and 0 if y > 0, f(UI) is the complete gamma function...
View articletitled, Age-Specific Death Rates With Tobacco Smoking and Occupational Activity: Sensitivity to Sample Length, Functional Form, and Unobserved Frailty
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for article titled, Age-Specific Death Rates With Tobacco Smoking and Occupational Activity: Sensitivity to Sample Length, Functional Form, and Unobserved Frailty
Journal Article
Demography (2001) 38 (1): 79–95.
Published: 01 February 2001
.... For example, gamma-Gompertz and more general gamma-Makeham models assume that individual hazards are a function of individual frailty and an exponen- tial function of age (see Horiuchi and Wilmoth 1998; Manton, Stallard, and Vaupel 1981). Specifically, in the gamma-Gompertz model the exponential function...
Journal Article
Demography (1991) 28 (4): 619–637.
Published: 01 November 1991
... the distribution of frailty or the shape of the underlying hazard. The procedure then is used to show that cohort mortality data from France are consistent with a generalized random-effects model in which frailty is gamma-distributed. nt]mis|Initial stages of this work were carried out at the University...
Journal Article
Demography (1977) 14 (1): 19–31.
Published: 01 February 1977
... of gamma pa- rameters representing the effects of the various independent variables, as well as a parameter representing the effect of the marginal distribution of the dependent variable itself. (The substantive meaning of these coefficients is discussed below.) Since the system analyzed here is recur...
Journal Article
Demography (1997) 34 (1): 31–48.
Published: 01 February 1997
... these equations the parameters of gamma distribu- tions can be represented as follows: It follows from this formula that if p, .jor O'~ .j..iO, then ~(X,X2) --t S(x,)S(x2 ) ; that is, the life spans T, and T2become mdependent. When P: = 1, Eq. (3) transforms to the well known shared frailty model (Clayton 1978...
Journal Article
Demography (1981) 18 (3): 389–410.
Published: 01 August 1981
... observation time is gamma distributed (Vaupel, 1979a). While this latter assumption is convenient because it simplifies the mathematics, these estimates can be obtained for any distribution which has a moment gener- ating function (MGF). To see this, it is necessary to examine the relationship be- tween...
Journal Article
Demography (1979) 16 (3): 439–454.
Published: 01 August 1979
... nature of the relationship between individual and cohort aging de- pends on the distribution of frailty among individuals. This paper assumes that frailty at birth is gamma distributed, with p.d.f.: 442 DEMOGRAPHY, volume 16, number 3, August 1979 fo(z) = Ak Zk-l . e-xzlr(k), (7) where A and k...
Journal Article
Demography (1981) 18 (2): 217–230.
Published: 01 May 1981
... which are constant over all individuals within the small population. Because direct mea- surements of the values of covariates for individuals are generally unavailable, we will assume that the variation in the pro- portional effects of unmeasured covariates can be represented by the two parameter gamma...
View articletitled, Methods for the Analysis of Mortality Risks Across Heterogeneous Small Populations: Examination of Space-Time Gradients in Cancer Mortality in North Carolina Counties 1970–75
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for article titled, Methods for the Analysis of Mortality Risks Across Heterogeneous Small Populations: Examination of Space-Time Gradients in Cancer Mortality in North Carolina Counties 1970–75
Journal Article
Demography (1998) 35 (4): 391–412.
Published: 01 November 1998
... world war (Horiuchi 1983). Amidst this confusion, however, the same two phases of change in the LAR curve are at least vaguely discernible: a shift upward from 1951-1955 to 1971-1975 and then a shift to the right from 1971-1975 to 1986-1990. FURTHER ANALYSIS USING THE GAMMA- MAKEHAM MODEL Upon first...
Journal Article
Demography (2018) 55 (4): 1363–1388.
Published: 05 July 2018
... at z = 1, Y ’s distribution approaches a Poisson with E ( Y ) = V ( Y ) = λ. It also includes the negative binomial distribution: if g ( z ) is a gamma density with E ( z ) = 1 and V ( z ) = 1 / θ, then Y has a negative binomial distribution with E ( Y ) = λ and V ( Y ) = λ + (λ 2 / θ...
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Journal Article
Demography (1987) 24 (3): 413–430.
Published: 01 August 1987
... discrete distributions, especially in the construction of models. Several continuous distributions have been fitted to age-specific fertility rates, for which quality of data is far superior to that of postpartum amenorrhea. They include Hadwiger, gamma, beta, Gompertz, and the Coale-Trussell fertility...
Journal Article
Demography (2015) 52 (3): 1035–1059.
Published: 12 May 2015
... interaction terms within a Poisson-gamma model, similar to non-Bayesian approaches of Smith et al. ( 2010 ) and Raymer et al. ( 2011b ). Concurrently, Wheldon et al. ( 2013 ) undertook Bayesian estimation and projection of populations to reconstruct past population data. Their approach is based...
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View articletitled, Bayesian Population Forecasting: Extending the Lee-Carter Method
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for article titled, Bayesian Population Forecasting: Extending the Lee-Carter Method
Includes: Supplementary data
Journal Article
Demography (2002) 39 (2): 287–310.
Published: 01 May 2002
... fertility and parity schedules. In each experiment, the period fertility rate schedule f(a,t) = (a,t) is a modified gamma density function with three parameters: TFR(t), the period total fertility rate; m(t), the period mean age of childbearing; and !(t), the period standard deviation in the age...
Journal Article
Demography (2013) 50 (6): 2053–2073.
Published: 01 August 2013
... ( y ij ). The B ij , which lie between 0 and 1, are known as shrinkage parameters because larger values shrink the conditional posterior mean mortality rates toward the structural mean. The gamma shape parameter ζ provides a measure of the influence of the structural mean. We adopt...
FIGURES
Journal Article
Demography (1994) 31 (3): 403–426.
Published: 01 August 1994
... of a wide variety of strictly nonnegative PDFs. Larsen and Vaupel prefer to use a gamma PDF because of its flexibility, but this specification has one important drawback: if the variance in fecundability is 0, the mean also must be O. Consequently the gamma model cannot be used in likelihood ratio tests...
Journal Article
Demography (1982) 19 (3): 291–299.
Published: 01 August 1982
... mixing distributions might be con- sidered appropriate. Spilerman (1972) suggested the use of a Gamma-distribu- tion within a continuous time migration DEMOGRAPHY, volume 19,number 3, August 1982 = Plt(P11 + (I - Pit) exp (lit -IltI, (8) (4) (5) (7) 294 logistic scaling functions of the form p, = Po(Po...
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