Handbook of the normal distribution:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1982
|
| Edition: | 1. print. |
| Series: | Statistics: textbooks and monographs
40 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 337 S. |
| ISBN: | 0824715411 |
Staff View
MARC
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| 100 | 1 | |a Patel, Jagdish K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Handbook of the normal distribution |c Jagdish K. Patel ; Campbell B. Read |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE v
1 GENESIS: A HISTORICAL BACKGROUND 1
2 SOME BASIC AND MISCELLANEOUS RESULTS 18
2.1 Definitions and Properties 18
2.2 Moments, Cumulants, and Generating Functions 22
2.3 Distributions Related to $(x) 24
2.4 Member of Some Well known Families of
Distribution 25
2.5 Compound and Mixed Normal Distribution 30
2.6 Folded and Truncated Normal Distributions:
Mills Ratio 33
2.7 Normal Distributions on the Circle 36
References 39
3 THE NORMAL DISTRIBUTION: TABLES, EXPANSIONS,
AND ALGORITHMS 43
3.1 Tables, Nomograms, and Algorithms 44
3.2 Expressions for the Distribution Function 50
3.3 Expressions for the Density Function 53
3.4 Continued Fraction Expansions: Mills Ratio 54
3.5 Expressions for Mills Ratio, Based on
Expansions 56
3.6 Other Approximations to Mills Ratio 62
3.7 Inequalities for Mills Ratio and Other
Quantities 63
3.8 Quantiles 66
3.9 Approximating the Normal by Other Distributions 69
References 71
vii
viii Contents
4 CHARACTERIZATIONS 77
4.1 Characterizations by Linear Statistics 78
4.2 Linear and Quadratic Characterizations 81
4.3 Characterizations by Conditional Distributions
and Regression Properties 84
4.4 Independence of Other Statistics 89
4.5 Characteristic Functions and Moments 90
4.6 Characterizations from Properties of
Transformations 91
4.7 Sufficiency, Estimation, and Testing 94
4.8 Miscellaneous Characterizations 98
4.9 Near characterizations 100
References 101
5 SAMPLING DISTRIBUTIONS 106
5.1 Samples Not Larger than Four 106
5.2 The Sample Mean: Independence 108
5.3 Sampling Distributions Related to Chi Square 109
5.4 Sampling Distributions Related to t 115
5.5 Distributions Related to F 119
5.6 The Sample Mean Deviation 122
5.7 The Moment Ratios v^ and b2 125
5.8 Miscellaneous Results 128
References 130
6 LIMIT THEOREMS AND EXPANSIONS 135
6.1 Central Limit Theorems for Independent
Variables 136
6.2 Further Limit Theorems 140
6.3 Rapidity of Convergence to Normality 149
6.4 Expansions 156
References 164
7 NORMAL APPROXIMATIONS TO DISTRIBUTIONS 168
7.1 The Binomial Distribution 169
7.2 The Poisson Distribution 176
7.3 The Negative Binomial Distribution 179
7.4 The Hypergeometric Distribution 183
7.5 Miscellaneous Discrete Distributions 186
7.6 The Beta Distribution 187
7.7 The von Mises Distribution 190
7.8 The Chi Square and Gamma Distributions 192
7.9 Noncentral Chi Square 196
7.10 Student s t Distribution 198
7.11 Noncentral t • 202
7.12 The F Distribution 205
7.13 Noncentral F 209
7.14 Miscellaneous Continuous Distributions 210
7.15 Normalizing Transformations 212
References 218
Contents ix
8 ORDER STATISTICS FROM NORMAL SAMPLES 224
8.1 Order Statistics: Basic Results 225
8.2 Moments 236
8.3 Ordered Deviates from the Sample Mean 243
8.4 The Sample Range 248
8.5 Quasi ranges 254
8.6 Median and Midrange 255
8.7 Quantiles 261
8.8 Miscellaneous Results 263
References 269
9 THE WIENER AND GAUSSIAN PROCESSES 275
9.1 Brownian Motion 275
9.2 The Wiener Process 276
9.3 Wiener Process with Absorbing Barriers 280
9.4 Gaussian Processes 282
9.5 The Ornstein Uhlenbeck Process 285
References 286
10 THE BIVARIATE NORMAL DISTRIBUTION 288
10.1 Definitions and Basic Properties 288
10.2 Tables and Algorithms 293
10.3 Offset Circles and Ellipses 300
10.4 Moments 308
10.5 Sampling Distributions 310
10.6 Miscellaneous Results 319
References 322
INDEX 329
|
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| isbn | 0824715411 |
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| physical | IX, 337 S. |
| publishDate | 1982 |
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| series2 | Statistics: textbooks and monographs |
| spelling | Patel, Jagdish K. Verfasser aut Handbook of the normal distribution Jagdish K. Patel ; Campbell B. Read 1. print. New York [u.a.] Dekker 1982 IX, 337 S. txt rdacontent n rdamedia nc rdacarrier Statistics: textbooks and monographs 40 Gauss, Loi de (Statistique) Normale verdeling gtt Statistiek gtt Statistik Gaussian distribution Normalverteilung (DE-588)4075494-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Normalverteilung (DE-588)4075494-7 s DE-604 Read, Campbell B. Verfasser aut Statistics: textbooks and monographs 40 (DE-604)BV000003265 40 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000022126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Patel, Jagdish K. Read, Campbell B. Handbook of the normal distribution Statistics: textbooks and monographs Gauss, Loi de (Statistique) Normale verdeling gtt Statistiek gtt Statistik Gaussian distribution Normalverteilung (DE-588)4075494-7 gnd |
| subject_GND | (DE-588)4075494-7 (DE-588)4151278-9 |
| title | Handbook of the normal distribution |
| title_auth | Handbook of the normal distribution |
| title_exact_search | Handbook of the normal distribution |
| title_full | Handbook of the normal distribution Jagdish K. Patel ; Campbell B. Read |
| title_fullStr | Handbook of the normal distribution Jagdish K. Patel ; Campbell B. Read |
| title_full_unstemmed | Handbook of the normal distribution Jagdish K. Patel ; Campbell B. Read |
| title_short | Handbook of the normal distribution |
| title_sort | handbook of the normal distribution |
| topic | Gauss, Loi de (Statistique) Normale verdeling gtt Statistiek gtt Statistik Gaussian distribution Normalverteilung (DE-588)4075494-7 gnd |
| topic_facet | Gauss, Loi de (Statistique) Normale verdeling Statistiek Statistik Gaussian distribution Normalverteilung Einführung |
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