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Matrix Operator

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Journal Article
Demography (1964) 1 (1): 56–73.
Published: 01 March 1964
... de poblicaón. Latent Root Matrix Operator Intrinsic Rate Population Projection Ordinary Method References 1. Leslie, P. H. “On the Use of Matrices in Certain Population Mathematics,” Biometrika , Vol. 33, pp. 184 ff. 2. Bernardelli, Harro. “Population Waves,” Journal...
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 (1966) 3 (2): 537–544.
Published: 01 June 1966
... : Office of Population Research, Princeton University . 4 Lopez Alvaro ( 1961 ). Problema in Stable Population Theory (pp. 36 – 40 ). Princeton : Office of Population Research, Princeton University . 5 Keyfitz Nathan ( 1964 ). The Population Projection as a Matrix Operator...
Journal Article
Demography (1969) 6 (3): 287–299.
Published: 01 August 1969
... multipliers, k being the number of schedules in the fertility sequence, and the survival rates in the mortality schedule. A numerical illustration of the theory is given using fertility data from Finland. 30 12 2010 © Population Association of America 1969 1969 Matrix Operator Successive...
Journal Article
Demography (1968) 5 (1): 382–409.
Published: 01 March 1968
... ). The Population Projection as a Matrix Operator . Demography , I , 56 – 73 . 10.2307/2060031 15 Murphy , E. M. ( 1966 ). The Latent Roots of the Population Projection Matrix . Demography , III , 259 – 75 . 10.2307/2060077 23 Pollard , J. H. ( 1966 ). On the Use of the Direct...
Journal Article
Demography (1966) 3 (1): 259–275.
Published: 01 March 1966
... Demography” (draft, mimeographed); “Matrix Multiplication as a Technique of Population Analysis,” The Milbank Memorial Fund Quarterly , XLII (October, 1964), 68–84; “The Population Projection as a Matrix Operator,” Demography , I (1964), 56–73. 3 E. M. Murphy, “A Generalization of Stable Population...
Journal Article
Demography (2023) 60 (6): 1675–1688.
Published: 01 December 2023
... on the transition probabilities as l x   = l x   −   1 P x   −   1   = l α ∏ k   =   α x   −   1 P k , (1) where the product operator ∏ k   =   α x   −   1 P k invokes matrix products. This survivorship function...
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Includes: Supplementary data
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
...–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 in Population , 13 , 123 – 150...
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Journal Article
Demography (1970) 7 (3): 341–348.
Published: 01 August 1970
... . Rogers , Andrei ( 1966 ). The multiregional matrix growth 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...
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
... of the relative precision of the projection. For a numerical study, 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...
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
... two 7 × 7 transition matrices. The first matrix is the standard transition matrix discussed earlier (see Tables  S3 – S6 in Online Resource 1). The standard transition matrix cross-tabulates tracts’ actual 1980 neighborhood types with their projected categories in 2010, assuming no change...
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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...