Contributions to order statistics:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Wiley
1962
|
| Schriftenreihe: | Wiley publications in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 482 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Contributions to order statistics |c ed. by Ahmed E. Sarhan ... |
| 264 | 1 | |a New York u.a. |b Wiley |c 1962 | |
| 300 | |a XXV, 482 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley publications in statistics | |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sarhān, Ahmad ʻIbādah |0 (DE-588)1164244264 |4 edt | |
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Datensatz im Suchindex
| _version_ | 1804117086125948928 |
|---|---|
| adam_text | Contents
CHAPTER PAGE
1 INTRODUCTION 1
1.1 The Scope of This Book 1
1.2 Outline of Contents 2
1.3 Some General Comments 7
PART I GENERAL THEORY (OVER ALL
SURVEY OF GENERAL NATURE)
2 DISTRIBUTION AND MOMENTS OF ORDER STATISTICS . . .11
2.1 Exact Distribution and Moments of Order Statistics . . 11
2.2 Asymptotic Distribution of Order Statistics . . . .15
3 GENERALIZED LEAST SQUARES THEOREM 20
3.1 Introduction ......... 20
3.2 Least Squares Estimates of Location and Dispersion
Parameters 21
3.3 Symmetrical Distributions 23
3.4 One Parameter Distributions 24
3.5 Relative Efficiencies of Sample Mean and /i* as Estimates
of Expectation ......... 25
xiii
Xiv CONTENTS
4 APPROXIMATION TO THE BEST LINEAR ESTIMATES .... 28
4A APPROXIMATION OF LEAST SQUARES ESTIMATES OF
LOCATION AND SCALE PARAMETERS ...... 28
4A.I Introduction ......... 28
4A.2 Linear Estimates Defined by a Continuous Weight
Function ......... 29
4A.3 Asymptotically Best Linear Estimates .... 29
4A.4 Application (Student Distribution) . . . . .31
4A.5 Remarks ......... 33
4A.6 Application for Small n . . . . . . .33
4B NEARLY BEST LINEAR ESTIMATES OF LOCATION AND
SCALE PARAMETERS ......... 34
4B.1 Introduction ......... 34
4B.2 Best Linear Estimates 34
4B.3 Unbiased Nearly Best Linear Estimates .... 35
4B.4 A Numerical Example ....... 39
4B.5 Censored Samples ........ 39
4B.6 The Efficiency of Nearly Best Linear Estimates ... 40
4B.7 Some Extensions and Modifications of the Method . . 43
4B.8 Some Remarks 44
5 ESTIMATION OF THE LOCATION AND SCALE PARAMETERS
BY SAMPLE QUANTILES (FOR LARGE SAMPLES) .... 47
5.1 Introduction ......... 47
5.2 Relative Efficiencies 48
5.3 The Best Linear Unbiased Estimators ..... 52
6 statistical theory of extreme values
(main results) ......... 56
6.1 Introduction ......... 56
6.2 Definitions 57
6.3 Exact and Asymptotic Properties ..... 60
6.4 Asymptotic Distributions ....... 65
6.5 The Three Types 70
CONTENTS XV
6.6 Extreme Order Statistics 75
6.7 Extremal Functions . . . . . . . .79
6.8 Bivariate Asymptotic Distributions of Extremes ... 83
7 SPECIAL PROBLEMS IN TESTING HYPOTHESES ..... 94
7A ORDER STATISTICS IN SHORT CUT TESTS ..... 94
7A.1 Introduction 94
7A.2 The Moments and Distribution of the Range and the
Studentized Range 95
7A.3 Approximations to Range and Mean Range in Small
Samples .97
7A.4 Tests on Variances 99
7A. 5 Substitute / Tests 101
7A.6 The Use of Range in the Analysis of Variance . . . 103
7A.7 Other Short cut Procedures Based on Order Statistics . 106
7A.8 Significance Test in Censored Samples . . . .108
7A.9 The Power Function of Tests Based on Range . . .109
7A.10 The Effect of Parent Nonnormality on Range Tests . .111
7B THE CLOSEST TWO OUT OF THREE OBSERVATIONS . . . .129
8 NONPARAMETRIC CONFIDENCE INTERVALS AND
TOLERANCE REGIONS . . . . . . . . .136
8.1 Introduction 136
8.2 Univariate Theory 136
8.3 Confidence Intervals for Percentage Points . . . .137
8.4 Univariate Tolerance Intervals . . . . . .138
8.5 Confidence Intervals for Median of Symmetrical
Population . . . . . . . . .139
8.6 Multivariate Tolerance Regions 140
9 MULTIPLE DECISIONS AND MULTIPLE COMPARISONS . . . 144
9.1 Introduction ......... 144
9.2 The Ranking of Means 144
9.3 Simultaneous Confidence Intervals ..... 148
9.4 Multiple Procedures on Variances . . . . .150
9.5 Short cut Methods 151
XVi CONTENTS
9.6 Selection Procedures Based on Multiple Comparisons
with a Standard ........ 151
9.7 Slippage Tests 153
9.8 Other Multiple Decision Procedures 155
9.9 Approximations to Upper Significance Points of Statis¬
tics Expressible as Maxima . . . . . .156
PART II SPECIFIC APPLICATIONS
10 NORMAL DISTRIBUTION . . . . . . . .165
10A THE MOMENTS OF THE ORDER STATISTICS AND OF THE
RANGE IN SAMPLES FROM NORMAL POPULATIONS . . . .165
10A.1 Introduction 165
10A.2 Hyperspherical Simplices and Their Relation to Trun¬
cated Multivariate Normal Distributions. . . .167
10A.3 Relation Between Moments of Order Statistics in
Normal Samples and Hyperspherical Simplices . .175
10A.4 Relation of the Moments of the Range and Product
Moments of Extreme Order Statistics in Normal
Samples to Hyperspherical Simplices . . . .183
10B TABLES OF LOWER MOMENTS OF ORDER STATISTICS
FOR SAMPLES FROM THE NORMAL DISTRIBUTION . . . .190
10B.1 Introduction 190
10B.2 Computation 190
10B.3 Tables 191
IOC THE BEST LINEAR ESTIMATES FOR THE PARAMETERS OF
THE NORMAL DISTRIBUTION 206
10C.1 Exact Estimates . 206
10C.2 Alternative Estimates 208
10C.3 Numerical Example ....... 212
10C.4 Comments 213
CONTENTS Xvii
10D SIMPLE ESTIMATES OF THE MEAN AND STANDARD
DEVIATION OF A NORMAL POPULATION ..... 269
10E DETERMINATIONS OF OPTIMUM SPACINGS IN THE CASE
OF NORMAL DISTRIBUTION ....... 272
10E.1 Introduction 272
10E.2 Location Parameter /j. ....... 272
10E.3 Scale Parameter a 275
10E.4 When Both the Location Parameter ft and the Scale
Parameter a Are Unknown ...... 277
10E.5 Optimum Grouping 277
10F ESTIMATION OF CORRELATION COEFFICIENT BY ORDER
STATISTICS ......... 283
10F.1 Introduction 283
10F.2 Estimation of p When Means and Standard Deviation
Are Known ......... 284
10F.3 Estimation of p When the Parameters Are Unknown . . 286
10F.4 The Use of Averages for Estimating p When the Vari¬
ance Ratio Is Known ....... 290
10G TESTS OF SIGNIFICANCE USING SAMPLE QUANTILES . . .291
10G.1 Introduction 291
10G.2 Student s Hypothesis 292
10G.3 Test of the Homogeneity of Several Means . . .293
10G.4 Selection of the Optimum Spacing for Testing Purposes . 295
10H REJECTION OF OBSERVATIONS ....... 299
10H.1 Tests Designed for Specific Types of Departures
from Normality 299
10H.2 General Discussion 299
10H.3 Sampling Assumptions 301
10H.4 Distributions of the Various Criteria . . . .304
10H.5 Power of the Various Criteria or Which Should
I Use? 305
10H.6 Performance of Criteria under Assumptions 4b and c . 307
xviii contents
10H.7 Performance of Criteria under Assumption Ad . .310
10H.8 Sampling from a Contaminated Population . . .312
10H.9 Attempts to Remove Bias 314
10H.10 Effects of Contamination on the Mean and Median . 314
10H.11 Bias of s2 and the Range 318
10H.12 Needed Research 321
11 EXPONENTIAL DISTRIBUTION ....... 343
11A MOMENTS OF ORDER STATISTICS ....... 343
11B BEST LINEAR UNBIASED ESTIMATES 352
11B.1 Estimates for 6 and a 352
11B.2 General Best Linear Unbiased Estimates for the One
Parameter Exponential Distribution . . . .354
11B.3 Estimation from a Multicensored Sample. . . . 354
11B.4 Estimation of Percentile Statistics ..... 356
11B.5 Estimates When Censoring Is from the Middle of the
Distribution......... 357
11C SIMPLE ESTIMATES OF THE PARAMETERS OF
EXPONENTIAL DISTRIBUTIONS ....... 361
11C.1 Introduction 361
11C.2 Some Results on Exponential Distributions . . . 361
11C.3 Simplified Estimates for the Mean of the One
Parameter Exponential Distribution .... 363
11C.4 Simplified Estimates for the Parameters of the Two
Parameter Exponential Distribution . . . .365
11C.5 Some Related Results 369
11D OPTIMUM SPACING AND GROUPING FOR THE
EXPONENTIAL DISTRIBUTION . . . . . . .371
11D.1 Optimum Spacing ....... 371
11D.2 Estimation Using the Best Two Observations . . . 379
11D.3 On Grouping for the One Parameter Exponential . . 379
HE TESTS OF SIGNIFICANCE AND CONFIDENCE INTERVALS . . . 380
CONTENTS Xix
12 OTHER DISTRIBUTIONS 383
12A RECTANGULAR DISTRIBUTION ....... 383
12A.1 The Moments of Order Statistics 383
12A.2 BLUE of 0x and 02 383
12A.3 Estimation of Percentiles 390
12B CERTAIN SYMMETRIC DISTRIBUTIONS 391
12B.1 The Moments of Order Statistics 391
12B.2 The Best Linear Unbiased Estimate 391
12C EXTREME VALUE DISTRIBUTION ...... 397
12C.1 The Three Asymptotic Types 397
12C.2 Estimation through Order Statistics . . . .398
12C.3 Statistical Estimation of the Endurance Limit, An
Application of Extreme Value Theory .... 406
12D GAMMA DISTRIBUTION .431
12D.1 Moments of the Arth Order Statistic . . . .431
12D.2 Best Linear Unbiased Estimates 434
12D.3 Some Remarks about the Distribution of the Arth
Order Statistic 434
12D.4 Applications to Life Testing, Reliability, and Other
Problems and Some Further Remarks . . . .437
12E RIGHT TRIANGULAR DISTRIBUTION ...... 450
12E.1 Moments of Order Statistics in Samples from a Right
Triangular Distribution ....... 450
12E.2 The Best Linear Estimates of the Parameters of the
Right Triangular Distribution. . . . . .451
References 454
Index 469
|
| any_adam_object | 1 |
| author2 | Sarhān, Ahmad ʻIbādah |
| author2_role | edt |
| author2_variant | a ʻ s aʻ aʻs |
| author_GND | (DE-588)1164244264 |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-07-09T15:48:48Z |
| institution | BVB |
| language | English |
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| spelling | Contributions to order statistics ed. by Ahmed E. Sarhan ... New York u.a. Wiley 1962 XXV, 482 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley publications in statistics Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Sarhān, Ahmad ʻIbādah (DE-588)1164244264 edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001747685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Contributions to order statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Contributions to order statistics |
| title_auth | Contributions to order statistics |
| title_exact_search | Contributions to order statistics |
| title_full | Contributions to order statistics ed. by Ahmed E. Sarhan ... |
| title_fullStr | Contributions to order statistics ed. by Ahmed E. Sarhan ... |
| title_full_unstemmed | Contributions to order statistics ed. by Ahmed E. Sarhan ... |
| title_short | Contributions to order statistics |
| title_sort | contributions to order statistics |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001747685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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