LEADER 04893nam 2200709 450 001 9910811329603321 005 20200520144314.0 010 $a1-118-85728-3 010 $a1-118-85737-2 035 $a(CKB)2550000001298090 035 $a(EBL)1687768 035 $a(SSID)ssj0001253374 035 $a(PQKBManifestationID)11709936 035 $a(PQKBTitleCode)TC0001253374 035 $a(PQKBWorkID)11293376 035 $a(PQKB)10863007 035 $a(MiAaPQ)EBC1687768 035 $a(Au-PeEL)EBL1687768 035 $a(CaPaEBR)ebr10870261 035 $a(CaONFJC)MIL608508 035 $a(OCoLC)879947306 035 $a(PPN)191455342 035 $a(EXLCZ)992550000001298090 100 $a20140927h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInformation and exponential families $ein statistical theory /$fO. Barndorff-Nielsen 205 $a2nd ed. 210 1$aChichester, England :$cJohn Wiley & Sons,$d2014. 210 4$dİ2014 215 $a1 online resource (250 p.) 225 1 $aWiley Series in Probability and Statistics 300 $aDescription based upon print version of record. 311 $a1-118-85750-X 311 $a1-306-77257-5 320 $aIncludes bibliographical references and indexes. 327 $aCover; Title Page; Copyright Page; Contents; CHAPTER 1 INTRODUCTION; 1.1 Introductory remarks and outline; 1.2 Some mathematical prerequisites; 1.3 Parametric models; Part I Lods functions and inferential separation; CHAPTER 2 LIKELIHOOD AND PLAUSIBILITY; 2.1 Universality; 2.2 Likelihood functions and plausibility functions; 2.3 Complements; 2.4 Notes; CHAPTER 3 SAMPLE-HYPOTHESIS DUALITY AND LODS FUNCTIONS; 3.1 Lods functions; 3.2 Prediction functions; 3.3 Independence; 3.4 Complements; 3.5 Notes; CHAPTER 4 LOGIC OF INFERENTIAL SEPARATION. ANCILLARITY AND SUFFICIENCY 327 $a4.1 On inferential separation. Ancillarity and sufficiency4.2 B-sufficiency and B-ancillarity; 4.3 Nonformation; 4.4 S-, G-, and M-ancillarity and -sufficiency; 4.5 Quasi-ancillarity and Quasi-sufficiency; 4.6 Conditional and unconditional plausibility functions; 4.7 Complements; 4.8 Notes; Part II Convex analysis, unimodality, and Laplace transforms; CHAPTER 5 CONVEX ANALYSIS; 5.1 Convex sets; 5.2 Convex functions; 5.3 Conjugate convex functions; 5.4 Differential theory; 5.5 Complements; CHAPTER 6 LOG-CONCAVITY AND UNIMODALITY; 6.1 Log-concavity 327 $a6.2 Unimodality of continuous-type distributions6.3 Unimodality of discrete-type distributions; 6.4 Complements; CHAPTER 7 LAPLACE TRANSFORMS; 7.1 The Laplace transform; 7.2 Complements; Part III Exponential families; CHAPTER 8 INTRODUCTORY THEORY OF EXPONENTIAL FAMILIES; 8.1 First properties; 8.2 Derived families; 8.3 Complements; 8.4 Notes; CHAPTER 9 DUALITY AND EXPONENTIAL FAMILIES; 9.1 Convex duality and exponential families; 9.2 Independence and exponential families; 9.3 Likelihood functions for full exponential families; 9.4 Likelihood functions for convex exponential families 327 $a9.5 Probability functions for exponential families9.6 Plausibility functions for full exponential families; 9.7 Prediction functions for full exponential families; 9.8 Complements; 9.9 Notes; CHAPTER 10 INFERENTIAL SEPARATION AND EXPONENTIAL FAMILIES; 10.1 Quasi-ancillarity and exponential families; 10.2 Cuts in general exponential families; 10.3 Cuts in discrete-type exponential families; 10.4 S-ancillarity and exponential families; 10.5 M-ancillarity and exponential families; 10.6 Complement; 10.7 Notes; References; Author index; Subject index 330 $aFirst published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions. 410 0$aWiley series in probability and statistics. 606 $aExponential families (Statistics) 606 $aSufficient statistics 606 $aDistribution (Probability theory) 606 $aExponential functions 615 0$aExponential families (Statistics) 615 0$aSufficient statistics. 615 0$aDistribution (Probability theory) 615 0$aExponential functions. 676 $a519.5 700 $aBarndorff-Nielsen$b O.$01724975 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811329603321 996 $aInformation and exponential families$94127493 997 $aUNINA