Advances in Growth Curve Models: Topics from the Indian Statistical Institute PDF
Preview Advances in Growth Curve Models: Topics from the Indian Statistical Institute
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 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. 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 LibraryofCongressControlNumber:2013943266 ©SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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
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