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Matrix Operator

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Journal Article
Demography (1968) 5 (1): 439–442.
Published: 01 March 1968
... teoría de poblaciones estables tratan con poblaciones cerradas. Summary The distribution of population among several age groups and regional locations is transformed from one time point to another by means of a matrix operator that was recently formulated by Rogers in this journal. Rogers discussed...
Journal Article
Demography (1964) 1 (1): 56–73.
Published: 01 March 1964
... ). Elementary Matrices . Cambridge, England : The University Press . THE POPULATION PROJECTION AS A MATRIX OPERATOR N. KEYFITZ University of Chicago RESUMEN El metodo de "componentes" para proyecciones de poblacion, uno de los meiodo« demogrtificos mas valiosos, ha sido tratado casi enteramente como maoda...
Journal Article
Demography (1966) 3 (2): 537–544.
Published: 01 June 1966
... ( 1964 ). The Population Projection as a Matrix Operator . Demography , I , 56 – 73 . 7 Andrei Rogers, “Matrix Analysis of Interregional Population Growth and Distribution,” Papers and Proceedings of the Regional Science Association , European Congress, Vienna, 1966 (in press). 8 Andrei...
Journal Article
Demography (1969) 6 (3): 287–299.
Published: 01 August 1969
... of the female population at t + w is given by the product M X F(O), where M is an appropriate matrix constructed using f and 8 and the sex ratio at birth (see Keyfitz, 1968, pp. 27-32). Let M(n), n = 1,2, k, represent the matrix operator constructed from the n-th fertility schedule and the common mortality...
Journal Article
Demography (1968) 5 (1): 382–409.
Published: 01 March 1968
..., "On the Generation and Growth of a Population," Sankya, VI (1942),93-96; P. H. Leslie, "On the Use of Matrices in Population Mathematics," Biometrika, XXXIII (1945), 183-212; N. Key- fitz, "The Population Projection as a Matrix Operator," Demography, I (1964), 56-73; E. M. Murphy, "The Latent Roots of the Population...
Journal Article
Demography (1966) 3 (1): 259–275.
Published: 01 March 1966
... Operator," Demog- raphy, I (1964), 56-73. IE. M. Murphy, "A Generalization of Stable Population Techniques" (unpublished Ph.D. dis- sertation, Department of Sociology, University of Chicago). of its characteristic equation, are essential to the matrix approach. The largest of these roots is equivalent...
Journal Article
Demography (1986) 23 (1): 91–104.
Published: 01 February 1986
.... The approach taken here assumes that a constant matrix operator acts on migration transition probabilities: Pt+ 1 = Pte. (1) By the usual convention, elements of the stochastic matrix P, give the probabilities that individuals beginning period t in origin i end it inj. Thus: ~ Pij = 1, V i, j 0::5 Pij ::5 1...
Journal Article
Demography (1965) 2 (1): 414–428.
Published: 01 March 1965
... in this direction, see Nathan Keyfitz, “The Population Projection as a Matrix Operator,” Demography , Vol. I, No. 1, 1964. COHORT FERTILITY VERSUS PARITY PROGRESSION AS METHODS OF PROJECTING BIRTHS DONALD S. AKERS Bureau of the Census RESUMEN El metoda corriente de elaboraci6n de proyecciones de la fecundidad...
Journal Article
Demography (2022) 59 (4): 1325–1352.
Published: 01 August 2022
...: The rise of divorce in the United States, 1980–2010 . Demography , 51 , 587 – 598 . Keyfitz N. ( 1964 ). The population projection as a matrix operator . Demography , 1 , 56 – 73 . Keyfitz N. ( 1986 ). Canadian kinship patterns based on 1971 and 1981 data . Canadian Studies...
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Includes: Supplementary data
Journal Article
Demography (1970) 7 (3): 341–348.
Published: 01 August 1970
... operator and the stable interregional age structure . Demography , 3 , 537 – 44 10.2307/2060178 . Rogers , Andrei ( 1968 ). Matrix Analysis of Interregional Population Growth and Distribution . Berkeley : University of California Press . DEMOGRAPHY Volume 7, Number 3 August 1970...
Journal Article
Demography (1967) 4 (2): 423–441.
Published: 01 June 1967
... length of the age-intervals. This length is the unit in which both age and time are measured. g See, for example, P. H. Leslie, op, cit. N. Keyfitz, "The Population Projection as a Matrix Operator," Demography, I (1964), 56-73; and N. Keyfitz and E. M. Murphy, Comparative Demographic Computations...
Journal Article
Demography (2013) 50 (5): 1615–1640.
Published: 17 September 2013
...-by-element product) is denoted by , and the Kronecker product is denoted by . The vec operator (e.g., vec X ) stacks the columns of a matrix into a column vector. See Caswell ( 2001 ) or Keyfitz and Caswell ( 2005 ) for an account of matrix models in demography. We consider s age classes. Let U...
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Includes: Supplementary data
Journal Article
Demography (1967) 4 (2): 515–531.
Published: 01 June 1967
... and by considering the possibility of “data smoothing.” 24 1 2011 © Population Association of America 1967 1967 Time Series Natural Increase Migration Operator Simplex Tableau Minimum Absolute Deviation References 1 Rogers , Andrei ( 1968 ). Matrix Analysis of Inter-regional...
Journal Article
Demography (1974) 11 (3): 473–481.
Published: 01 August 1974
... ). The Multiregional Matrix Growth Operator and the Stable Interregional Age Structure . Demography , 3 , 537 – 544 . 10.2307/2060178 Rogers Andrei ( 1973 ). The Multiregional Life Table . Journal of Mathematical Sociology , 3 , 127 – 138 . 10.1080/0022250X.1973.9989827 Rogers Andrei...
Journal Article
Demography (1971) 8 (2): 185–194.
Published: 01 May 1971
... A. ( 1968 ). Matrix Analysis of Interregional Population Growth and Distribution . Berkeley, Cal. : University of California Press . Rogers A. ( 1969 ). On perfect aggregation in the matrix cohort-survival model of interregional population growth . Journal of Regional Science , 9 , 417...
Journal Article
Demography (1971) 8 (4): 441–450.
Published: 01 November 1971
..., Norwegian population data is used. where M is the (m + 1) X (m + 1) "projection matrix" Fo F l F l F.. M= Po 0 0 0 0 p l 0 The type of population projection which we are about to study, is of the usual type, and is constructed in the following way: The present population is counted and the vector eo gives...
Journal Article
Demography (1990) 27 (3): 337–356.
Published: 01 August 1990
... are calculated. 7 To obtain these tables, we first use the matrix of the transition rates (Mx) to calculate a transition probability matrix, P" by (Rogers & Ledent 1976) (5) This allows us to specify the familiar life table relationship from which survivorship values for all ages from 55 on up can be calculated...
Journal Article
Demography (2016) 53 (6): 1933–1953.
Published: 24 October 2016
.... Table 3 Observed transition matrix in multiethnic metropolitan areas, 1980–2010 Tract Category in 1980 Tract Category in 2010 nw w w+h/a wha wb wb+h/a wbha Total nw 1,692 0 8 13 22 68 143 1,946 w 16 199 340 199 34 133 199 1,120 w+h/a 190 60 903 541 18...
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Includes: Supplementary data
Journal Article
Demography (2005) 42 (3): 537–558.
Published: 01 August 2005
...], a a a a a with matrix shrinkage factor where the V( ) terms are now K X K covariance matrices and E(ea ) is a K X 1 vector of means. As before, small shrinkage adjustments are made by the e a estimator in areas where local rates are expected to be estimated precisely, and vice versa. As in the scalar case, EB...
Journal Article
Demography (1968) 5 (1): 449–459.
Published: 01 March 1968
... wholesal- ing center), 5. Multiple brand stocking = f. (sales, man- ufacturers-importer merchandising, and wholesale merchandising). The measures are defined in Appendix Il, which also presents a matrix-equation for- mulation and a discussion of statistical 9 W. F. Massy, "Television Ownership in 1950...