scholarly journals A Mixture Model Incorporating Individual Heterogeneity in Human Lifetimes

2021 ◽  
Author(s):  
Fei Huang ◽  
Ross Maller ◽  
Brandon Milholland ◽  
Xu Ning

AbstractAnalysis of some extensive individual-record data using a demographically informed model suggests constructing a general population model in which the lifetime of a person, beyond a certain threshold age, follows an extreme value distribution with a finite upper bound, and with that upper bound randomized over the population. The resulting population model incorporates heterogeneity in life-lengths, with lifetimes being finite individually, but with extremely long lifespans having negligible probability. Our findings are compared in detail with those of related studies in the literature, and used to reconcile contradictions between previous studies of extreme longevity. While being consistent with currently reported analyses of human lifetimes, we nevertheless differ with those who conclude in favour of unbounded human lifetimes.

2018 ◽  
Vol 48 (1) ◽  
pp. 337-374
Author(s):  
Paul A. Jargowsky ◽  
Christopher A. Wheeler

Researchers studying income inequality, economic segregation, and other subjects must often rely on grouped data—that is, data in which thousands or millions of observations have been reduced to counts of units by specified income brackets. The distribution of households within the brackets is unknown, and highest incomes are often included in an open-ended top bracket, such as “$200,000 and above.” Common approaches to this estimation problem include calculating midpoint estimators with an assumed Pareto distribution in the top bracket and fitting a flexible multiple-parameter distribution to the data. The authors describe a new method, mean-constrained integration over brackets (MCIB), that is far more accurate than those methods using only the bracket counts and the overall mean of the data. On the basis of an analysis of 297 metropolitan areas, MCIB produces estimates of the standard deviation, Gini coefficient, and Theil index that are correlated at 0.997, 0.998, and 0.991, respectively, with the parameters calculated from the underlying individual record data. Similar levels of accuracy are obtained for percentiles of the distribution and the shares of income by quintiles of the distribution. The technique can easily be extended to other distributional parameters and inequality statistics.


2019 ◽  
Vol 56 (2) ◽  
pp. 574-589
Author(s):  
László Györfi ◽  
Norbert Henze ◽  
Harro Walk

AbstractLet X1, …, Xn be independent random points drawn from an absolutely continuous probability measure with density f in ℝd. Under mild conditions on f, wederive a Poisson limit theorem for the number of large probability nearest-neighbour balls. Denoting by Pn the maximum probability measure of nearest-neighbour balls, this limit theorem implies a Gumbel extreme value distribution for nPn − ln n as n → ∞. Moreover, we derive a tight upper bound on the upper tail of the distribution of nPn − ln n, which does not depend on f.


2019 ◽  
Vol 40 (Supplement_1) ◽  
Author(s):  
B B Loegstrup ◽  
T Ellingsen ◽  
A B Pedersen ◽  
B Darvalics ◽  
H E Botker ◽  
...  

Abstract Purpose To examine whether the risk of cardiovascular disease (heart failure (HF), ischemic heart disease (IHD), myocardial infarction (MI), and coronary revascularization) in patients with rheumatoid arthritis (RA) is comparable to the risk in patients with diabetes mellitus (DM) and general population. Methods The study included the entire Danish population encompassing about 5.7 million inhabitants. Through individual record linkage of nationwide administrative health registries, the authors identified subjects who developed RA and DM and compared these to a matched general population. The cohorts were followed from 1 January 1995 until December 2016. Results The study population consisted of a cohort of 15,491 RA patients, 309,698 DM patients, and a general population cohort of 77,455 subjects matched by age, sex, and year of diagnosis with the RA cohort. Cumulative incidence for HF, IHD, MI, PCI (percutaneous coronary intervention) and CABG (coronary artery bypass grafting) are shown in figure 1. The adjusted hazard ratio (HR) for diagnosis of HF within the 10-year observational period for RA (1.46; 95% CI 1.34–1.59) and DM (1.86; 95% CI 1.78–1.95) were increased compared to the general population. Comparing the risk of HF within the follow-up period a 21% relative risk (HR 0.79, 95% CI 0.73–0.85) reduction of HF in RA compared to DM patients was observed. The HR for IHD development during the follow-up period for RA (1.36; 95% CI 1.25–1.48) and DM (1.64; 95% CI 1.58–1.72) were increased compared to control group. Comparing the risk of IHD within the follow-up period a 17% relative risk (HR 0.83, 95% CI 0.77–0.89) reduction for IHD development in RA compared to DM patients. The HR for MI was increased both in RA (1.48; 95% CI 1.34–1.63) and DM (1.57; 95% CI 1.49–1.65) compared to the control group, without any statistical difference within RA and DM. According to the coronary revascularization, comparable increased numbers of PCI were observed in RA (1.37; 95% CI 1.22–1.54) and DM (1.50; 95% CI 1.41–1.59) patients compared to control subjects. Interestingly, the HR of coronary by-pass grafting (CABG) for RA (1.20; 95% CI 0.98–1.49) and DM (1.99; 95% CI 1.80–2.19) resulting in an adjusted 39% relative risk (0.61 95% CI 0.50–0.74) reduction for CABG in RA compared to DM patients. Figure 1 Conclusions Patients with RA are at increased risk of cardiovascular disease when compared to the general population although slightly lower than observed among patients with DM. Revascularization with CABG was only increased among DM patients, which likely reflects physician compliance to guidelines recommending CABG in case of multivessel disease among DM patients. Patients with RA should be considered for prophylactic strategies in the same way as recommended for patients with DM.


1977 ◽  
Vol 109 (10) ◽  
pp. 1359-1374 ◽  
Author(s):  
Y. Wang ◽  
A. P. Gutierrez ◽  
G. Oster ◽  
R. Daxl

AbstractA general population model for cotton growth and development is presented. The model captures the essential properties of the biological processes, and is sufficiently flexible to the incorporation of complex physiological and behavioral characteristics. The model has been used successfully to simulate the growth and development of Acala SJ-II cotton in California. The mathematical framework for coupling plants and herbivores has been presented, and the biological implications of their damage to the plant examined in a very general way.


1984 ◽  
Vol 54 (3) ◽  
pp. 915-920
Author(s):  
Bernard J. Gallagher ◽  
Brian J. Jones ◽  
Joseph A. McFalls

The records of 1174 mentally retarded people were analyzed with regard to patterns of seasonality of birth. A population model was derived from birth records of the general population born during the same time period as the mentally retarded people. Log-linear analyses uncovered no significant differences between the seasons of birth for the mentally retarded and those in the general population. There were also no significant relationships when the data were analyzed by race and sex. Given the sample size and the sophistication of the analytic model, these results have important implications for an unresolved literature.


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