Introduction to the Mathematics of Demography

260 Pages·1993·57.988 MB·English

by  Robert L. Brown

INTRODUCTION
tot he
MATHEMATICS
of
DEMOGRAPHY
(S ecoEnddi tion)
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TABOLFE
CONTENTS
Preface vii
Chapt1e r 1
DATA:S OURCEASN DE RRORS
1.1I ntroduc1 tion
1.2T heC ollecotfDi eomno graphic 2S tatistics
1.3T akitnhgCe e nsu5s
1.4S ourocfeE sr roarnsdT heCiorr rect7i ons
1.4C.o1v erEargreo r7s
1.4.C2o nteonrRt e spoEnrsreo r8s
1.4.M3i sstatoefmA egne9t
1.4.P4r ocesEsrirnogr1 s2
1.4.S5a mpling Errors 12
1.4.G6r osErsr Roart io/ENrertRo art i1o4
1.5C onclus1i5o n
1.6E xerci1s6e s
Chapt2e r 21
MEASUREOSF MORTALITAYN DF ERTILITY
2.1I ntroduction 21
2.2C rudRea te2s2
2.3A ge-SpeMcoirfitcaR laitteys 24
2.4A djusMteeads uorfeM so rtal2i4t y
2.5M easuorfIe nsf aMnotr tal2i7t y
2.6A ge-SpeFceirfitciR laittey2s 9
27. Exerci3s e7s
iv TabolfCe o ntents
Chapt3er 45
THE LIFE TABLE
3.1 Introduction 45
3.2 Life Table Values 46
3.3 The Continuous Case 50
3.4 Methods for Fractional Ages 56
3.4.1 Uniform Distribution of Deaths 57
3.4.2 Constant Force of Mortality 58
3.5 Exercises 62
Chapt4e r 65
CONSTRUCTION OF LIFE TABLES FROM CENSUS DATA
4.1 Introduction 65
4.2 The 1979-81 U.S. Life Tables 68
4.2.1 Ages Under 2 Years 68
4.2.2 Ages 2 to 4 and 5 to 94 Years 70
4.2.3 Ages Over 94 Years 71
4.2.4 Derivation of Other Values 74
4.3 The 1985-87 Canadian Life Tables 76
4.3.1 Infant Tables 77
4.3.2 Adult Tables 80
4.4 Aqridged Life Tables 84
4.5 Analysis of the Life Table by Cause of Death 89
4.6 Exercises 91
Chapt5e r 97
STATIONARY POPULATION THEORY
5.1 Introduction 97
5.2 Analysis of the Survivorship Group 98
5.3 The Stationary Population 103
5.4 The Lexis Diagram 112
5.5 Further Applications 119
5.6 Exercises 123
TabloefC ontents v
Chapt6e r
127
STABLPEO PULATITOHNE ORY
6.1I ntrodu1ct2i7o n
6.2T heF oundatoifSo tnasb le Populat1i2o8n Theory
6.3A pproximraift rionCmge nsDuast a1 37
6.4A pplicat1i4o5n s
6.5Q uasi-Stable P1o4p8u lations
6.6 Exer1c5i1s es
Chapt7e r
159
POPULATIPORNO JECTIONS
7.1I nter-CaenndIs mamle diPaotset -CeEnsstailm a1t5e9s
7.1L.i1n eIanrt erpol1a5t9i on
7.1P.o2l ynoImnitaelr pol1a6t0i on
7.1.G3e ometric M1o6d0e ling
7.2P opulation PTrhoejL eocgtiisCotunirscv :1e 6 3
7.3P opulation PTrhoejC eocmtpioonMneesnt:th o1d6 8
7.4E xerci17s 7e s
Chapt8e r
187
USESO FC ENSUDSA TA
8.1I ntroduc1t8i7o n
8.2A PractEixcaamlp lFeu:n diSnogc iSaelc ur1i8t8y
8.3C onclus2i0o2n
8.4E xerci2s0e3s
AppendAi x
207
DERIVATIOOFNE QUATIO(N1 .3)
AppendBi x
209
THE1 979-U8.1SL .I FTEA BLES
LifTea blfeoM ra le2s0 9
LifTea blfeoF re mal2e1s3
vi TabolfCe o ntents
AppendCi x 217
THE1 985-C8A7N ADIANL IFTEA BLES
LifTea blfeot rh Fei rYseta orfL if(eM ale2)17
LifTea blfeot rh Fei rYseta orfL ife( Femal2e1)8
AdulLti feT abl(eM ale2)1 9
AdulLti feT abl(eF emal2e2)3
AppendDi x 227
FURTHEDRI SCUSSOIFON
STABLPEO PULATITOHNE ORY
Solvfoirnr g 2 27
NumeriVcaalluo efrs 229
TheR enewEaqlu ati2o3n0
AnswetroEs x ercises 231
Bibliography 239
Index 243
PREFACE
Ins piotfea ni ncreaisnetde raensdpt u blicaatcitoinvi intt yh e
genersaulb jeacrteoa f d emograap hmya,j ovro isdt irlelm ainas :
suitatbelxet btoooi kn troduuncdee rgrasdtuuadteetn ott hsme a the­
matiocfds e mography.
Textboaonkdsj ournpaalp eornst het opoifcd emography
wiltly pichaalvloeyn eo ft wob asifocu ndatisoonuarlc eMsa.n y
fintdh ebiars iinss ociolaongday r,ae l moesntt irdeelsyc riapntdi ve
qualitiantp irvees entaTthieontn h.e riesa widvea rieotfty e xts
andp apewrrsi ttfernoa m m athematpiecraslp ecbtuittv hee,as er e
ofteeint hdeerv ooiftd h ede scrimpattievreni eacle ssfoarar s yo und
pedagogpirceasle ntoartt ihoeanyr, ae d vancweodr kmso rseu itable
fogrr aducaotuer ses.
to
Thitse xta,p propricaatlelIlenydt roducttihoeMn a the­
matiocfDs e mogratprhityeo,ss triakh ea ppcyo mprombiestew eae n
qualitparteisveen taantdii notnr oducutnodreyr,g raqduuaanttei ta­
tivaen alysTihse.ri esm uchm atertihaalit s p uredleys criptive,
butt heriesa lsaone xtenssuirvveoe fyt hefo undatimoantahle ma­
ticrse quiirnem du cho ft hew orkd onbe yd emographTehres .
mathematciocnatlec natnb eu nderstboyou dn dergrasdtuua­te
dentwsi tah backgrooufna dl gebirnat,r oduccatlocruyal nuds ,
introdupcrtoobrayb ility.
Examplaersde rawfnr oNmo rtAhm ericaapnp licaatnido ns
studiEeasc.ch h apter iann culmubdeoerfws o rkeexda mpalnedsa
seotf e xercfoirst ehser eadteors olvMea.n yo ft het exetx ercises
appearoenrd e ceCnotu r1s6e1 e xaminatgiiovnebsny t heS ociety
ofA ctuarTiheesip.re rmistsoii onnc ltuhdeeqs uee stiinto hnte e xt
isg reaatplpyr eciated.
Thea uthwoirs hteosa cknowltehdegh ee aviyn flueonnc e
thitse xotfp redecewsosrokbrsy K eyfit[z1 5P]o,l laYruds,u afn,d
viii Preface
Poll[a2r2da] n,dK eyfiatnzd B eekm[a1n6 T]h.e l aswta se speci­
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Thea uthwoirs hteots h anakn umbeorfp rofessiwohnoa ls
reviesweevde drraalfo tfts h tee xatn dm advea luacbolnet ributions
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