Advances in Growth Curve Models: Topics from the Indian Statistical Institute

278 Pages·2013·4.986 MB·English

by  Ratan Dasgupta (auth.), Ratan Dasgupta (eds.)

Springer Proceedings in Mathematics & Statistics
Ratan Dasgupta Editor
Advances in
Growth Curve
Models
Topics from the Indian Statistical Institute
Springer Proceedings in Mathematics & Statistics
Volume 46
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Ratan Dasgupta
Editor
Advances in Growth Curve
Models
Topics from the Indian Statistical Institute
123
Editor
RatanDasgupta
IndianStatisticalInstitute
Professor,TheoreticalStatistics
andMathematicsUnit
Kolkata,India
ISSN2194-1009 ISSN2194-1017(electronic)
ISBN978-1-4614-6861-5 ISBN978-1-4614-6862-2(eBook)
DOI10.1007/978-1-4614-6862-2
SpringerNewYorkHeidelbergDordrechtLondon
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Preface
A growth curve is an empirical model of the evolution of a quantity over time.
Growth curve models (GCM) in longitudinal studies are widely used in many
disciplinesbesidesbiology,particularlyinstatistics,populationstudies,economics,
biological sciences, statistical quality control, environment, sociology, nano-
biotechnology, fluid mechanics and for quantities such as population size, body
height, biomass, and fungal growth. An important precursor of the GCM is the
classical GCM considered by S N Roy and R. Potthoff in early 1960s and C R
Raoaboutthesametime. Thatleadstothe developmentofrepeatedmeasurement
designs,longitudinalmodels,andrelatedevolutionarymodelsinepidemiologyand
bioinformatics.EventheChaostheorycomesundersuchmodels.Ithasimportant
applicationsinpsychometryandpsychiatry.Theevolutionarymodelsarealsoakin
toGCM.GrowthandnutritionofIndianchildrenhasnotimprovedmuchinspiteof
India’seconomicprosperity.
This conference proceeding presents some ideas about the research works on
GCM that is going on by the scientists of Indian Statistical Institute in different
branchesof science. The genesisof this workstarted severalyearsbackwhen the
editorandhiscolleaguesconductedgrowthexperimentsin theagriculturalfirm at
IndianStatisticalInstitute,Giridih,Jharkhand;atribalarea.AtthattimeEditortook
academic&administrativeresponsibilityofISIGiridihasCoordinatoronthethird
tier in a three-tier administrative system. Continued research for several years on
plantgrowthposedsometheoreticalandappliedproblemsthatarerecordedinthis
proceeding. We also thought it will be a nice idea if the researchers working in
GCMhadanopportunitytoexchangeideasabouttheirfieldofinterest.Tothisend,a
workshopwasorganizedintheyear2011thatwasfollowedbyanationalconference
onGCMintheyear2012atGiridih.AnotherworkshoponGCMwasconductedat
ISIGiridihduring21-22March,2013.Weinvitedsomewell-knownresearchersto
contributeto thisconferenceproceedingandfurtherinvitedthe participantsofthe
conferencetosubmitmorethanonepaper,ifpossiblefortheproceedings.Allthe
paperswere peer reviewed.The resultis the compilationof 15 papersin different
v
vi Preface
branchesofscienceinthisproceeding.Theendeavorwillbeconsideredsuccessful
if this can give some idea aboutsolving theoreticaland practical problemsin this
broadareaofGCMtowhichmanyresearchersareinterestedin.
December2012 RatanDasgupta
Kolkata,India
Contents
1 YamGrowthExperimentandAbove-GroundBiomass
asPossiblePredictor ....................................................... 1
RatanDasgupta
2 SomeStatisticalPerspectivesofGrowthModelsinHealth
CarePlans................................................................... 35
PranabK.Sen
3 TestingofGrowthCurveswithCubicSmoothingSplines ............. 49
TapioNummiandNicholasMesue
4 Nonuniform Rates of Convergence to Normality
forTwo-SampleU-StatisticsinNonIIDCasewithApplications..... 61
RatanDasgupta
5 CorrelatedBivariateLinearGrowthModels:Optimal
DesignsforSlopeParameterEstimation................................. 89
P.S.S.N.V.P.RaoandBikasK.Sinha
6 Optimal-TimeHarvestofElephantFootYamandRelated
TheoreticalIssues........................................................... 101
RatanDasgupta
7 Evolution of Scour and Velocity Fluctuations
DuetoTurbulenceAroundCylinders.................................... 131
H.Maity,R.Dasgupta,andB.S.Mazumder
8 SouthPoleOzoneProfileandLowerToleranceLimit.................. 149
RatanDasgupta
9 ANewTechniqueforEstimatingPopulationDistribution
of Growth Curve Parameters with Longitudinal
andCross-sectionalData .................................................. 171
SedighehMirzaeiSalehabadiandDebasisSengupta
vii
viii Contents
10 TuberCropGrowthandParetoModel .................................. 185
RatanDasgupta
11 Effect of Past Demographic Events on the mtDNA
DiversityAmongtheAdiTribeofArunachalPradesh,India......... 199
S.KrithikaandT.S.Vasulu
12 GrowthCurveModelinRelationtoExtremalProcesses
BasedonStationaryRandomVariables ................................. 215
RatanDasgupta
13 ProjectionofIndianPopulationbyUsingLeslieMatrix
withChangingAgeSpecificMortalityRate,AgeSpecific
FertilityRateandAgeSpecificMaritalFertilityRate.................. 227
PrasantaPathakandVivekVerma
14 GrowthCurveAnalysisofCumulativeAutomobileDefects........... 241
RatanDasguptaandAvinashDharmadhikari
15 GrowthandNutritionalStatusofPre-SchoolChildren:
AComparativeStudyofJharkhand,BiharandWestBengal......... 257
SusmitaBharati,ManoranjanPal,andPremanandaBharati
ix
Fig.1 YamcormsortingbeforeplantationinGiridihfarm
Fig.2 EcologicalobservatoryinISIGiridihFarm