Order Statistics, Third Edition PDF
Preview Order Statistics, Third Edition
Onder Statistics This Bin WILEY SERIES IV MROBAMILITY AND STATISTICS Esublabed by WALTER A. SUEWHTAHTand SAMUBL S. WILkS said 1 Balding Not 4. ©. Cra, Nichols Fisker, In lactone. Rasen Lote M Ayan, Dvd Son (kbion Snith dal ie Pete Leos RnctiVe farac £ Shuart Mater, ov Kendall ‘A compli fhe ies in his serie appears tthe end of thi oka Order Statistics Third Edition HA. pavID ot Sate Cats Department of etter ‘ames HN. NAGARAJA, Bre Oo Sine Coeriy Papa f Sie Catunbue, OF Gas INTERSCIENCE AJOVIN SILY 2 S08, INC. PUBLICATION. se et ut tees acne eee See ee ee ee oman IST RGIaceemecmae Lint etn ny ete pi ob hea hin ‘ety ris Nowy ay 2 soe anda yah eaten ny es iy of Cou Cats abit Dae (Bar eabren eons genoa To Ruth—HAD To my mother, Susheela—HNN Contents PREFACE INTRODUCTION LT The subject of onder sausitex 12. The scope and limits of this book 13 Notation 4 Byerises BASIC DISTRIBUTION THEORY 2 Distribution of single andor statistic 2.2 Joint distribution af hwo oF more onder staistcs 23 Distribution of the range ened of ether systematic. 24 Onder statistics for a diserete parent 2S Conditional distributions, onder statistics as Markov chain, and independence results 26 Related satstics 27 Exercises EXPECTED VALUES AND MOMENTS BL Baste foruuloe 42 Spaciat consinuots distributions 33° The discrete case 324 Recurrence relations 5 Rrercises BOUNDS AND APPRUXIMATIONS FOR MOMENTS ‘OF ORDER STATISTICS 4.1 Introduction 42 Distribasion-free bounds for the moments of order 43 44 45 46 a7 statistics ond of the range Bounds and appresimations by orthogonal inverse expunsion Stochastic orderings Bounds forthe expected values of enter statistics in erm of quantiles ofthe parent distraction Apprasimations to momen in terms ofthe quantile Fenelon and is derivaives Exercises ‘THE NONIID CASE 31 $2 36 Introduction Onder statistics for independent nonidentically discribueed variates Order staisties for dependent variates Inequalities and recurrence relations—nam-HD cases Ronnds for linear functians of under statistics and for their expected values Rxercises FURTHER DISTRIBUTION THEORY fa 62 63 64 65 66 Iravoduetion Stadentication Statitics expressible ax mums Random division of un interval Linear functions of ander statinion Moving onder statisties conrens 67 Charaterizations 1? 68 Concomizants of onder staistics yaa 69 Exercises 18 ‘ORDER STATISTICS IN NONPARAMETRIC INFERENCE 159 71 Distritusion free confidence intervals for quantiles 159 7.2 Distribution free totorance intorvats 164 7.3 Distribution free prediction intervals 167 74° Exercises 169 ORDER STATISTICS IN PARAMETRIC INFERENCE 171 81 Introduction and basic results 178 82 Information in onder statistics 180 83 Bootverap estimation of quanctes and of moments of tarde statistics 183 84 Least-squares extimation of lovation and scale parameters by onder statistics 185 5 Estimation of location and scale parameters for censored data it 86 Life tening, with special emphasis on the expmentiat distribution 204 87 Prediction of onder statistics 208 88 Robust extimation a 89° Brercises 223 SHORTCUT PROCEDURES 238 DL Imroducrion 239 22 Quick measures of tcation 2a 9.3 Range and mean range as measures oftispersion 242 94 Other quick measures of dispersion 248 25 Quick esimanes in bivariate samples 250 9.6 The sudensced range 258 97 Quick teas 2357 98 Ranbed-vet sampling 262 0 it covrenns wo 919 gat 92 O-staistcs and L-moments in date summertzatton Probability plowing and tess of goodness of ft Statistical quatiy coneot Exercises ASYMPTOTIC THEORY Ir 402 103 joa 105 108 107 108 109 Introduction Representations for the ceniral sample quantes Asymptotic joint distribution of central quantiles Optimal choice of order seatiticn ix large samples The asympotc distribution ofthe extreme ‘The asympiotc joist disiribtation of extremes Extreme-value thuory for dependent sequences Asymprotic propertics of intermediate order siaristes Asymptotic results for multivariate samples 10.10 Baercives ASYMPTOTIC RESULTS FOR FUNCTIONS OF ORDER STATISTICS us uz 3 ud us ué m7 us Introduction Asympiotie distribution ofthe range, midrange, and spacings Limit distribution of the eimned mean Asymptutic normality of linear functions of onder Gptimat asymptonc estimation by order statisties Estimarors of tai index and extreme quansites Asymptotic theory of concomiants of order statistics Exercives APPENDIX: GLTDY. TO TABLES AND ALGORITHMS REFERENC) Bu 33 3S 323 323 ide 29 337 335 sar 35 350 385 367 451 Preface to Third Edition Sse the pale io WE the one einnn 3 this Bode ath they an sepleatons of onl watinies have realy expanded. this ion Chaps 2-9 eal with eit-snple theory, eth dvs uo ditbarion tars (Chapters 2-81 ‘nd sata inteence ‘Chapter 7-9). Axympllie su e boat in Chagos 1D sod IL representing a ouling in cover Tribe spice previ ations te penetin esi ap op t-dae account of what we aya ay he enue he suet of ede tation. Many special tpist real sen op, fa or Uwe re ty erly pie on intact far ee texteosive aveouts eis ‘heavier of refer hn tort fi) LADD i he Second ws aur! 1500, al th in sto a Ee sina of & good mans referages cited eae, Been so, we bad to omit a larger propoon cf elevant refereaces dm bere, ging sume prelerencec papers ac previly memnored Sn revew aide, Taio ta nena ny asin capone wory al stasis coer tan aon sapiens (Chee), Dillon ection are emerge Dew: 2.6, Relotd sis. 44, Srochic cing 6 6. Moving order state 67, Ghasscofzatcas, 73. Disuibuion es predtionimervas: £2. Information Fnandersati wen 83, Noopirapetimaten; 9.6, Steaua: ings 9. Ranked set seeping: and 89. Oveatnon and £ monensin date summarcatun, Sectin 65 inetndos jr app ican redial ltr} Seton 96 bHoeinsleneeteatig
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