Mathematical statistics with applications in R PDF
Preview Mathematical statistics with applications in R
Mathematical Statistics with Applications in R Mathematical Statistics with Applications in R Second Edition By Kandethody M. Ramachandran Chris P. Tsokos AMSTERDAM (cid:129) BOSTON (cid:129) HEIDELBERG (cid:129) LONDON NEW YORK (cid:129) OXFORD (cid:129) PARIS (cid:129) SAN DIEGO SAN FRANCISCO (cid:129) SINGAPORE (cid:129) SYDNEY (cid:129) TOKYO Academic Press is an imprint of Elsevier AcademicPressisanimprintofElsevier 32JamestownRoad,LondonNW17BY,UK 525BStreet,Suite1800,SanDiego,CA92101-4495,USA 225WymanStreet,Waltham,MA02451,USA TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK Secondedition2015 Copyright#2015,2009ElsevierInc.Allrightsreserved Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinany formorbyanymeanselectronic,mechanical,photocopying,recordingorotherwisewithout thepriorwrittenpermissionofthepublisherPermissionsmaybesoughtdirectlyfrom Elsevier’sScience&TechnologyRightsDepartmentinOxford,UK:phone(þ44)(0)1865 843830;fax(þ44)(0)1865853333;email:[email protected] submityourrequestonlinebyvisitingtheElsevierwebsiteathttp://elsevier.com/locate/ permissions,andselectingObtainingpermissiontouseElseviermaterial. 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ISBN:978-0-12-417113-8 Dedicated to our families: Usha, Vikas, Vilas, and Varsha Ramachandran and Debbie, Matthew, Jonathan, and Maria Tsokos Acknowledgments We express our sincere appreciation to our late colleague, co-worker, and dear friend,ProfessorA.N.V.Rao,forhishelpfulsuggestionsandideasfortheinitialver- sionofthesubjecttextbook.Inaddition,wethankBong-jinChoiandYongXufor their kind assistance in the preparation of the first edition of the manuscript. We would like to thank the following for their help in preparation of this edition: A.K.M.R.Bashar,JasonBurgess,MudithaPerera,JoelNegron,HansapaniRodrigo, DooYoungKim,TaysseerSharaf,BhikhariTharu,RamKafle,DrRebeccaWooten, andDrOlgaSavchuk.Wealso,wouldliketothankallthosecommentedonourbook intheinternetplacessuchasAmazonandGooglesites,likeMansahAlkebu-lanfor thepositivecommentsandespeciallytoDrAxelBoldtforhisdetailedreviewonthe first edition. We also wish to acknowledge the contributions of all of the editorial staff of ELSEVIER, Jill Cetel, Anusha Sambamoorthy, and others, who at various stages helped in completion of this book. Finally, we acknowledge our students at the University of South Florida for their useful comments through the years. To all ofthem, we are very thankful. Kandethody M. Ramachandran Chris P. Tsokos Tampa, FL xv About the Authors KandethodyM.RamachandranisProfessorofMathematicsandStatisticsatthe University of South Florida. He received his BS and MS degrees in Mathematics from the Calicut University, India. Later, he worked as a researcher at the Tata Institute of Fundamental Research, Bangalore center, at its Applied Mathematics Division. Dr Ramachandran got his PhD in Applied Mathematics from Brown University. Hisresearchinterestsareconcentratedintheareasofappliedprobabilityandsta- tistics.Hisresearchpublicationsspanavarietyofareassuchascontrolofheavytraf- fic queues, stochastic delay equations and control problems, stochastic differential games and applications, reinforcement learning methods applied to game theory and other areas, software reliability problems, applications of statistical methods to microarray data analysis, and mathematical finance. He is also co-author with ChrisTsokosofabooktitledStochasticDifferentialGamestheoryandApplications, AtlantisPress. ProfessorRamachandran isextensivelyinvolved inactivities toimprovestatis- ticsandmathematicseducation.HeisarecipientoftheTeachingIncentiveProgram awardattheUniversityofSouthFlorida.HeisamemberoftheMEMECollabora- tive,whichisapartnershipamongmathematicseducation,mathematics,andengi- neeringfacultytoaddressissuesrelatedtomathematicsandmathematicseducation. HewasalsoinvolvedinthecalculusreformeffortsattheUniversityofSouthFlorida. Heisrecipientof2milliondollargrantfromNSF,and1.4milliongrantfromHHMI toimprove STEM education at USF. ChrisP.TsokosisDistinguishedUniversityProfessorofMathematicsandStatistics at the University of South Florida. He received his BS in Engineering Sciences/ Mathematics, his MA in Mathematics from the University of Rhode Island, and hisPhDinStatisticsandProbabilityfromtheUniversityofConnecticut.Professor Tsokos has also served on the faculties at Virginia Polytechnic Institute and State Universityand the University ofRhodeIsland. Dr Tsokos’s research has extended into a variety of areas, including stochastic systems, statistical models, reliability analysis, ecological systems, operations research,timeseries,Bayesiananalysis,andmathematicalandstatisticalmodeling ofglobalwarming,amongothers.Heistheauthorofmorethan250researchpub- lications inthese areas. ProfessorTsokosistheauthorofseveralresearchmonographsandbooks,includ- ingRandomIntegralEquationswithApplicationstoLifeSciencesandEngineering, ProbabilityDistribution: An IntroductiontoProbabilityTheory withApplications, MainstreamsofFiniteMathematicswithApplications,ProbabilitywiththeEssential xvii xviii About the Authors Analysis,andAppliedProbabilityBayesianStatisticalMethodswithApplicationsto Reliability,among others. Dr Tsokos is the recipient of many distinguished awards and honors, including FellowoftheAmericanStatisticalAssociation,USFDistinguishedScholarAward, SigmaXiOutstandingResearchAward,USFOutstandingUndergraduateTeaching Award,USFProfessionalExcellenceAward,URIAlumniExcellenceAwardinSci- ence and Technology, Pi Mu Epsilon, and election to the International Statistical Institute, among others. Preface to Second Edition Inthesecondedition,whilekeepingmuchofthematerialfromthefirstedition,there aresomesignificantchanges andadditions. DuetothepopularityofRanditsfree availability, we have incorporated R-codes throughout the book. This will make it easierforstudentstodothedataanalysis.Wehavealsoaddedachapterongoodness of fit tests and illustrated their applicability with several examples. In addition we haveintroducedmoreprobabilitydistributionfunctionswithrealworlddatadriven applicationsinglobalwarming,brainandprostatecancer,nationalunemployment, andtotalrainfall.Inthisedition,wehaveshortenedthepointestimationchapterand merged itwith intervalestimation. Inaddition,manycorrectionsandadditions are madetoreflect the continuous feedback we have obtained. We have created a student companion website, http://booksite.elsevier.com/ 9780124171138,with solutions toselected problemsand dataon Globalwarming, brainandprostatecancer,nationalunemployment,andtotalrainfall.Wehavealso posted solutions to most of the problems in the instructor site, http://textbooks. elsevier.com/web/Manuals.aspx?isbn¼9780124171138. PREFACE TO FIRST EDITION This textbook is of an interdisciplinary nature and is designed for a one- or two- semester course in probability and statistics, with basic calculus as a prerequisite. The book is primarily written to give a sound theoretical introduction to statistics whileemphasizingapplications.Ifteachingstatisticsisthemainpurposeofatwo- semestercourseinprobabilityandstatistics,thistextbookcoversalltheprobability conceptsnecessaryforthetheoreticaldevelopmentofstatisticsintwochapters,and goes ontocoverallmajor aspects ofstatisticaltheoryintwosemesters,insteadof only a portion of statistical concepts. What is more, using the optional section on computerexamplesattheendofeachchapter,thestudentcanalsosimultaneously learntoutilizestatisticalsoftwarepackagesfordataanalysis.Itisouraim,without sacrificing any rigor, to encourage students to apply the theoretical concepts they have learned. There are many examples and exercises concerning diverse applicationareasthatwillshowthepertinenceofstatisticalmethodologytosolving real-worldproblems.Theexampleswithstatisticalsoftwareandprojectsattheendof thechapterswillprovidegoodperspectiveontheusefulnessofstatisticalmethods.To introduce the students to modern and increasingly popular statistical methods, we haveintroducedseparatechaptersonBayesiananalysisandempiricalmethods. One of the main aims of this book is to prepare advanced undergraduates and beginning graduate students in the theory of statistics with emphasis on interdisci- plinaryapplications.Theaudienceforthiscourseisregularfull-timestudentsfrom mathematics, statistics, engineering, physical sciences, business, social sciences, materialsscience,andsoforth.Also,thistextbookissuitableforpeoplewhowork xix xx Preface to Second Edition inindustryandineducationasareferencebookonintroductorystatisticsforagood theoretical foundation with clear indication of how to use statistical methods. Tra- ditionally,oneofthemainprerequisitesforthiscourseisasemesteroftheintroduc- tion to probability theory. A working knowledge of elementary (descriptive) statisticsisalsoamust.Inschoolswherethereisnostatisticsmajor,imposingsuch abackground,inadditiontocalculussequence,isverydifficult.Mostofthepresent books available on this subject contains full one-semester material for probability and then, based on those results, continue on to the topics in statistics. Also, some ofthesebooksinclude intheir subject matter only the theoryofstatistics,whereas otherstakethecookbookapproachofcoveringthemechanics.Thus,evenwithtwo fullsemestersofwork,manybasicandimportantconceptsinstatisticsarenevercov- ered.Thisbookhasbeenwrittentoremedythisproblem.Wefusetogetherbothcon- ceptsinorderforthestudenttogainknowledgeofthetheoryandatthesametime develop the expertise tousetheir knowledgein real-worldsituations. Althoughstatisticsisaveryappliedsubject,thereisnodenyingthatitisalsoa veryabstractsubject.Thepurposeofthisbookistopresentthesubjectmatterinsuch awaythatanyonewithexposuretobasiccalculuscanstudystatisticswithoutspend- ing two semesters of background preparation. To prepare students, we present an optionalreviewoftheelementary(descriptive)statisticsinChapter1.Alltheprob- abilitymaterialrequiredtolearnstatisticsiscoveredintwochapters.Studentswitha probabilitybackgroundcaneitherrevieworskipthefirstthreechapters.Itisalsoour belief that any statistics course is not complete without exposure to computational techniques.Attheendofeachchapter,wegivesomeexamplesofhowtouseMini- tab, SPSS, and SAS to statistically analyze data. Also, at the end of each chapter, thereareprojectsthatwillenhancetheknowledgeandunderstandingofthematerials coveredinthatchapter.Inthechapterontheempiricalmethods,wepresentsomeof themoderncomputationalandsimulationtechniques,suchasbootstrap,jackknife, andMarkovchainMonteCarlomethods.Thelastchaptersummarizessomeofthe stepsnecessarytoapplythematerialcoveredinthebooktoreal-worldproblems.The first eight chapters have been class tested as a one-semester course for more than 3 years with five different professors teaching. The audience was junior- and senior-level undergraduate students from many disciplines who had two semesters ofcalculus,mostofthemwithnoprobabilityorstatisticsbackground.Thefeedback from the students and instructors was very positive. Recommendations from the instructors and students were very useful in improving the style and content of the book. AIM AND OBJECTIVE OF THE TEXTBOOK This textbook provides a calculus-based coverage of statistics and introduces stu- dentstomethodsoftheoreticalstatisticsandtheirapplications.Itassumesnoprior knowledgeofstatisticsorprobabilitytheory,butdoesrequirecalculus.Mostbooks atthislevelarewrittenwithelaboratecoverageofprobability.Thisrequiresteaching Preface to Second Edition xxi onesemesterofprobabilityandthencontinuingwithoneortwosemestersofstatis- tics. This creates a particular problem for nonstatistics majors from various disci- plines who want to obtain a sound background in mathematical statistics and applications.Itisouraimtointroducebasicconceptsofstatisticswithsoundtheo- reticalexplanations.Becausestatisticsisbasicallyaninterdisciplinaryappliedsub- ject, we offer many applied examples and relevant exercises from different areas. Knowledgeofusingcomputersfordataanalysisisdesirable.Wepresentexamples of solving statistical problems using Minitab, SPSS, andSAS. FEATURES (cid:129) During yearsof teaching, we observedthat manystudents who do well in mathematicscoursesfindit difficulttounderstand the conceptof statistics. To remedy this, we present mostof the materialcoveredin the textbook with well-defined step-by-stepprocedures tosolvereal problems.Thisclearly helps the studentsto approach problem solvinginstatistics more logically. (cid:129) Theusefulness ofeach statisticalmethod introduced isillustrated byseveral relevantexamples. (cid:129) Atthe endof each section,we provide ample exercises that are a goodmixof theory andapplications. (cid:129) Ineachchapter,wegivevariousprojectsforstudentstoworkon.Theseprojects aredesignedinsuchawaythatstudentswillstartthinkingabouthowtoapplythe resultstheylearnedinthechapteraswellasotherissuestheywillneedtoknow for practical situations. (cid:129) Attheendofthechapters,weincludeanoptionalsectiononcomputermethods with Minitab, SPSS, andSAS exampleswith clear and simple commands thatthe student can usetoanalyze data. This will help the student tolearn how toutilize the standard methods they have learned in the chapter to study real data. (cid:129) We introducemany ofthe modernstatistical computational and simulation concepts,suchasthejackknifeandbootstrap methods,theEMalgorithms, and the Markov chain MonteCarlomethods such asthe Metropolis algorithm,the Metropolis-Hastingsalgorithm, andthe Gibbs sampler.TheMetropolis algorithm was mentioned in Computingin Science andEngineering asbeing amongthetop10algorithmshavingthe“greatestinfluenceonthedevelopment andpractice of science and engineeringinthe 20th century.” (cid:129) WehaveintroducedtheincreasinglypopularconceptofBayesianstatisticsand decision theorywith applications. (cid:129) Aseparatechapteron design ofexperiments, including a discussion on the Taguchi approach, isincluded. (cid:129) Thecoverage of the book spans mostofthe important concepts instatistics. Learningthematerialalongwithcomputationalexampleswillpreparestudentsto understandand utilize software procedures toperform statisticalanalysis.
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