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#### Linear Formula

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Journal Article
Demography (1984) 21 (4): 613–622.
Published: 01 November 1984
... competing formulas may be small. 9 1 2011 © Population Association of America 1984 1984 Life Table Linear Formula Abridge Life Table Life Table Death French Male References Farr W. ( 1864 ). English Life Table . London : Longman . Gompertz B. ( 1825...
Journal Article
Demography (2002) 39 (1): 65–73.
Published: 01 February 2002
...Joshua R. Goldstein Abstract In this article, I derive a simple formula for approximating the ultimate size of a population that undergoes a gradual transition to replacement fertility. I model the fertility transition by specifying a linear frontier on the Lexis surface across which a change...
Journal Article
Demography (1966) 3 (2): 528–536.
Published: 01 June 1966
... consider the condition under which the four equations linear in the constants: YI/ Y2 1 0 Y2 - YI =0. HIGHER-ORDER DETERMINANTAL FORMULAS IN POWERS OF x The advantage of determinants be- comes apparent in the several directions The element in the lower right is called a divided difference. Expanding the de...
Journal Article
Demography (1977) 14 (2): 239–241.
Published: 01 May 1977
... established. Furthermore, since \lea) \lea. b) = \l(b)' (8) the relationship is not restricted to \l for a single population. Given the mathematical relationship between \l and ~ , the log-linear formula- tion enjoys all of the advantages Schoen outlined for \l: (a) each population has a real number as its...
Journal Article
Demography (1975) 12 (2): 313–324.
Published: 01 May 1975
...., Jordan, 1967,p. 273) An appropriate integration formula must be selected to express the niL", in terms of the il Once that is done, an algebraic solution for the model can be obtained in a straightforward manner. For example, take the simple linear case where The procedure begins at age 0, where the ilo...
Journal Article
Demography (2002) 39 (2): 287–310.
Published: 01 May 2002
.... At this point, readers should wonder: how was the linear formula derived, why does it work, and under what circum- stances is it likely to produce accurate rate estimates? The next sections address these issues. MATHEMATICAL DERIVATION Cohort Change in V Suppose that for each individual there is a set...
Journal Article
Demography (1964) 1 (1): 74–82.
Published: 01 March 1964
... of general formula proved clumsy for other than linear fitting and for attempts to translate the mean. Because the basic statistical measures are relative moments, the formulae were developed again, this time using a separate poly- nomial fit for the total, and proportion of that total in each separate age...
Journal Article
Demography (2019) 56 (5): 1975–2004.
Published: 28 August 2019
... the direction of one temporal slope, we can in many cases make conclusions about the direction and magnitude of at least one of the other slopes. The top part of Table 2 shows the simplified form of the bounding formulas when only the sign of a single linear effect is considered. Table 2 APC bounds...
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Includes: Supplementary data
Journal Article
Demography (1966) 3 (1): 259–275.
Published: 01 March 1966
... into n/2 real quadratic factors if n is even and (n - 1)/2 real quadratic factors and a real linear factor if n is odd. We will work with quadratic factors to avoid complex arithmetic. The complex roots of the factors can be found directly by the quadratic formula. Processes to find the roots directly...
Journal Article
Demography (1978) 15 (4): 625–635.
Published: 01 November 1978
... in the calculation of the other life tables were obtained from the published values by the formula 633 M n x All tables used a radix of 100,000 and the U.S. life table values for £1' The values for the proposed method were computed using, for ages over 1, the formulas shown in Chart 1. The linear tables assumed 4al...
Journal Article
Demography (1972) 9 (3): 515.
Published: 01 August 1972
... the in- terval is large. If simplicity is the main issue why not settle for the still simpler formula generated by the assumption that P(x) is a linear function of x, for which not even the tables of exponential functions are necessary. Fergany may wish to compare the results shown in his Table...
Journal Article
Demography (1979) 16 (3): 455–473.
Published: 01 August 1979
... these ages accord- ing to the proportion of ever-born chil- dren in each age category. The formula was: 0* = BIRTHS(20-24)2 + BIRTHS(25-29)3 BIRTHS(20-29) It can easily be shown that, if the cumula- tive mortality values are linear within unit intervals, it would follow that 4(0*) is a weighted average of 4...
Journal Article
Demography (1990) 27 (1): 165–174.
Published: 01 February 1990
... linear formulas for estimating the ages of children from the number of deciduous teeth erupted are not useful. The tooth eruption curve is a straight line only when eruption percentages are plotted against the logarithm of postconception age (E. Hunt, personal 168 Demography, Vol. 27, No.1, February 1990...
Journal Article
Demography (1976) 13 (2): 287–290.
Published: 01 May 1976
...Andrel Rogers; Jacques Ledent 26 1 2011 © Population Association of America 1976 1976 Life Table Apply System Analysis Simultaneous Linear Equation Life Table State Life Table Cohort References Rogers Andrei ( 1975 ). Introduction to Multiregional Mathematical...
Journal Article
Demography (1968) 5 (1): 439–442.
Published: 01 March 1968
... in-migration ratio. Having solved (6) for A, we may sub- stitute it into formula (7) and solve the following system of linear equations (Gt - XI)W = 0, (7a) to get W. The ratio of any two compo- nents of W remains constant over all non- trivial solutions of W. Thus, in the stable population (defined...
Journal Article
Demography (1971) 8 (3): 335–339.
Published: 01 August 1971
... of the continuation function could be im- proved substantially by making the effective decay rate an exponential function of age. Theoretical reasoning was presented to justify these empirical results. I C -r'= ae or oral contraceptive acceptors who are still active to time can be approximated by the general formula...
Journal Article
Demography (1972) 9 (3): 443–453.
Published: 01 August 1972
... of the estimate of (PIS) used in apply- ing the above formula. A variant of the ratio procedure just described is the following. First, estimate the ratio PT/Pa, where P'l' stands for the population in year T (the year for which an estimate is required) and Po for the known population count in the immediately...
Journal Article
Demography (2022) 59 (2): 587–605.
Published: 01 April 2022
... approximation formula for a 1 0 in low-mortality contexts, which aims to incorporate differences in preterm birth through a proxy measure—the ratio of infant to under-five mortality. Models are built and tested using data from the Human Mortality Database. Model results and validation show that the newly...
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Includes: Supplementary data
Journal Article
Demography (1971) 8 (3): 341–352.
Published: 01 August 1971
...' in Taiwan (calculated by substituting va 9. 800 and u-O.0334 in formula (4» Stochastic Approach to Estimation of IUD Prevalence 345 (8) (9) has been a gradual upward trend, which may be assumed to be a linear function of time. Assuming this linear trend would con- tinue, and that the monthly rate...
Journal Article
Demography (1978) 15 (4): 523–539.
Published: 01 November 1978
... ). On the Analogy Between Linear and Log-Linear Regression . Ann Arbor : Department of Statistics, University of Michigan . Edwards , A. W. F. ( 1964 ). The Measure of Association in a 2 × 2 Table . Journal of the Royal Statistical Society, Series A , 126 , 109 – 114 . 10.2307/2982448...