Advances on models, characterizations, and applications

Advances on Models, Characterizations and Applications......Page 1
STATISTICS: Textbooks and Monographs......Page 4
Preface......Page 5
Contributors......Page 11
Contents......Page 8
CONTENTS......Page 14
1.1 INTRODUCTION......Page 15
1.2.1 Definitions and duality......Page 17
1.2.2 Monotone h. f. and r. h. f.......Page 18
1.2.3 Truncation......Page 19
 1.3.1 The shapes of a doublet of p. d. f. and h. f. ( or r. h. f.)......Page 20
1.3.2 The shapes of a triplet......Page 22
1.3.3 Four- interval description......Page 24
1.4 SUFFICIENCY OF RESTRICTIONS......Page 25
1.4.2 Examples of monotone shapes......Page 26
1.4.3 General shapes......Page 28
1.5 ADDITIONAL NOTES......Page 29
REFERENCES......Page 30
ABSTRACT......Page 32
2.1 INTRODUCTION......Page 33
2.2 STOCHASTIC ORDERING AND A. S. CONSTRUCTION OF RANDOM VARIABLES......Page 36
2.3 FRECHET BOUNDS— EXTREMAL RISK......Page 42
2.4 Δ-MONOTONE, SUPERMODULAR, AND DIRECTIONALLY CONVEX FUNCTION CLASSES......Page 54
REFERENCES......Page 61
ABSTRACT......Page 69
3.1 INTRODUCTION......Page 70
3.2 q-NUMBERS, q-FACTORIALS, AND q-STIRLING NUMBERS......Page 71
3.3 q-FACTORIAL MOMENTS......Page 73
3.4 A CHARACTERIZATION OF THE EULER DISTRIBUTION......Page 79
REFERENCES......Page 82
ABSTRACT......Page 84
4.1 INTRODUCTION......Page 85
4.2 CHARACTERIZATION USING LEFT AND RIGHT TRUNCATION......Page 86
4.3 CHARACTERIZATIONS FOR SOME IMPORTANT DISTRIBUTIONS......Page 90
REFERENCES......Page 91
ABSTRACT......Page 93
5.1 INTRODUCTION......Page 94
5.2 PRELIMINARIES......Page 96
5.3 CHARACTERIZATION RESULT......Page 98
REFERENCES......Page 103
CONTENTS......Page 107
6.1 INTRODUCTION......Page 108
6.2 THE CHARACTERIZATIONS......Page 109
REFERENCES......Page 118
ABSTRACT......Page 120
7.1 INTRODUCTION......Page 121
7.2 REGRESSING ORDER STATISTICS......Page 124
7.3 REGRESSING RECORD VALUES......Page 126
REFERENCES......Page 128
CONTENTS......Page 130
8.1 INTRODUCTION......Page 131
8.2 CHARACTERIZATIONS BASED ON TRUNCATED EXPECTATIONS......Page 134
8.2.1 An extended version of the Oakes– Dasu result......Page 137
8.3.1 Characterization based on equality of distribution......Page 138
8.3.2 Characterization based on expectation of functions of order statistics......Page 144
8.3.3 Further characterization results based on ordered random variables......Page 149
8.4 CHARACTERIZATION OF GPDS BASED ON RELEVATION TYPE EQUATION......Page 151
8.5 CHARACTERIZATION OF GPDS BASED ON RESIDUAL UNCERTAINTY......Page 154
REFERENCES......Page 155
ABSTRACT......Page 161
9.1 INTRODUCTION......Page 162
9.2 RESULTS......Page 163
REFERENCES......Page 167
CONTENTS......Page 169
10.1 INTRODUCTION......Page 170
10.2 THE CURIOUS CLASSICAL MULTIVARIATE NORMAL MODEL......Page 171
10.3 NORMAL CONDITIONAL DISTRIBUTIONS......Page 172
10.4 NON- NORMAL CONDITIONALS......Page 175
10.5 HIDDEN TRUNCATION MODELS......Page 177
10.6 NON- NORMAL VARIANTS......Page 180
10.7 SURVIVAL MODELS INVOLVING HIDDEN TRUNCATION......Page 181
10.8 EVEN MORE FLEXIBILITY......Page 182
REFERENCES......Page 183
ABSTRACT......Page 185
11.1 INTRODUCTION......Page 186
11.2 CHARACTERIZATION......Page 187
REFERENCES......Page 194
ABSTRACT......Page 196
12.1 INTRODUCTION......Page 197
12.2 THE DIFFERENTIAL EQUATION......Page 198
12.3 SOME PROPERTIES OF THE EIGENFUNCTIONS......Page 199
12.4 THE FIRST PRINCIPAL COMPONENT......Page 200
12.5 AN INEQUALITY......Page 201
12.6 THE LOGISTIC DISTRIBUTION......Page 202
12.7 DEGREE OF INDEPENDENCE......Page 203
REFERENCES......Page 205
ABSTRACT......Page 207
13.1 INTRODUCTION......Page 208
13.2 THE MODEL AND ESTIMATORS......Page 210
13.3 RISK PERFORMANCE OF ˜β i UNDER THE LINEX LOSS FUNCTION......Page 212
APPENDIX......Page 214
REFERENCES......Page 217
ABSTRACT......Page 220
14.1 INTRODUCTION......Page 221
14.2 DISTRIBUTION OF RfD......Page 223
14.3 PROPERTIES OF THE RfD DISTRIBUTION......Page 226
14.4.1 Equal spacing......Page 227
14.4.2 Geometric dosing......Page 228
14.5 NUMERICAL ILLUSTRATION......Page 229
14.6 DISCUSSION......Page 234
REFERENCES......Page 236