A first course in order statistics:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM, Society for Industrial and Applied Mathematics
2008
|
| Edition: | Unabridged republ. of the work 1. publ. 1992 |
| Series: | Classics in applied mathematics
54 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Originally published: New York : Wiley, c1992 |
| Physical Description: | XXIII, 279 S. graph. Darst. |
| ISBN: | 9780898716481 |
Staff View
MARC
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| 245 | 1 | 0 | |a A first course in order statistics |c Barry C. Arnold ; N. Balakrishnan ; H. N. Nagaraja |
| 250 | |a Unabridged republ. of the work 1. publ. 1992 | ||
| 264 | 1 | |a Philadelphia |b SIAM, Society for Industrial and Applied Mathematics |c 2008 | |
| 300 | |a XXIII, 279 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Classics in applied mathematics |v 54 | |
| 500 | |a Originally published: New York : Wiley, c1992 | ||
| 534 | |c 1992 | ||
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Record in the Search Index
| _version_ | 1804137752916131840 |
|---|---|
| adam_text | Contents
Preface
to the Classics Edition
xiii
Further Reading
xiv
Preface
xv
Acknowledgments
xvii
Notations and Abbreviations
xix
Errata
xxiii
1.
Introduction and Preview
1
1.1.
Order Statistics,
1
1.2.
Here, There, and Everywhere,
4
2.
Basic Distribution Theory
9
2.1.
Introduction,
9
2.2.
Distribution of an Order Statistic,
9
2.3.
Joint Distribution of Two Order Statistics,
16
2.4.
Some Properties of Order Statistics,
21
2.5.
Distribution of the Median, Range, and Some Other
Statistics,
27
Exercises,
34
3.
Discrete Order Statistics
41
3.1.
Introduction,
41
3.2.
Single Order Statistic,
41
3.3.
Joint Probability Mass Function,
45
3.4.
Dependence Structure,
48
3.5.
Distribution of the Range,
50
3.6.
Geometric Order Statistics,
51
3.7.
Order Statistics from a Without-Repiacement Sample,
53
Exercises,
56
χ
CONTENTS
4.
Order Statistics from some Specific Distributions
63
4.1.
Introduction,
63
4.2.
Bernoulli Distribution,
63
4.3.
Three-Point Distribution,
65
4.4.
Binomial Distribution,
66
4.5.
Poisson
Distribution,
70
4.6.
Exponential Distribution,
72
4.7.
Uniform Distribution,
78
4.8.
Logistic Distribution,
81
4.9.
Normal Distribution,
86
4.10.
Computer Simulation of Order Statistics,
95
Exercises,
97
5.
Moment Relations, Bounds, and Approximations
107
5.1.
Introduction,
107
5.2.
Basic Formulas,
108
5.3.
Some Identities and Recurrence Relations,
110
5.4.
Universal Bounds,
120
5.5.
Series Approximations,
128
Exercises,
132
6.
Characterizations Using Order Statistics
141
6.1.
Who Cares?,
141
6.2.
The Distribution of an Order Statistic Determines the Parent
Distribution,
142
6.3.
Characterizations Based on Moments of Order
Statistics,
143
6.4.
Characterizations Based on Distributional Relationships
among Order Statistics,
146
6.5.
Characterizations Involving Dependency Assumptions,
153
6.6.
Characterizations Involving Samples of Random Size,
155
Exercises,
157
7.
Order Statistics in Statistical Inference
159
7.1.
Introduction,
159
7.2.
Types of Order Statistics Data,
160
7.3.
Order Statistics and Sufficiency,
162
7.4.
Maximum-Likelihood Estimation,
167
CONTENTS
ХІ
7.5. Linear
Estimation
of Location and Scale Parameters,
171
7.6.
Prediction of Order Statistics,
180
7.7.
Distribution-Free Confidence and Tolerance Intervals,
183
7.8.
Goodness-of-Fit Tests,
186
7.9.
Other Applications,
189
Exercises,
194
8.
Asymptotic Theory
205
8.1.
Need and History,
205
8.2.
Exponential Order Statistics,
207
8.3.
Sample Maximum and Minimum,
208
8.4.
Other Extreme Order Statistics,
217
8.5.
Central and Intermediate Order Statistics,
223
8.6.
Linear Functions of Order Statistics,
227
Exercises,
234
9.
Record Values
241
9.1.
The Hottest July 4th On Record!,
241
9.2.
Definitions
and Preliminary Results on
Record Statistics,
242
9.3.
Distribution of the nth Upper Record,
243
9.4.
Distributions of Other Record Statistics,
245
9.5.
Record Range,
248
9.6.
Bounds on Mean Record Values,
249
9.7.
Record Values in Dependent Sequences,
251
9.8.
Records in Improving Populations,
252
Exercises,
254
Bibliography
259
Author Index
271
Subject Index
275
|
| adam_txt |
Contents
Preface
to the Classics Edition
xiii
Further Reading
xiv
Preface
xv
Acknowledgments
xvii
Notations and Abbreviations
xix
Errata
xxiii
1.
Introduction and Preview
1
1.1.
Order Statistics,
1
1.2.
Here, There, and Everywhere,
4
2.
Basic Distribution Theory
9
2.1.
Introduction,
9
2.2.
Distribution of an Order Statistic,
9
2.3.
Joint Distribution of Two Order Statistics,
16
2.4.
Some Properties of Order Statistics,
21
2.5.
Distribution of the Median, Range, and Some Other
Statistics,
27
Exercises,
34
3.
Discrete Order Statistics
41
3.1.
Introduction,
41
3.2.
Single Order Statistic,
41
3.3.
Joint Probability Mass Function,
45
3.4.
Dependence Structure,
48
3.5.
Distribution of the Range,
50
3.6.
Geometric Order Statistics,
51
3.7.
Order Statistics from a Without-Repiacement Sample,
53
Exercises,
56
χ
CONTENTS
4.
Order Statistics from some Specific Distributions
63
4.1.
Introduction,
63
4.2.
Bernoulli Distribution,
63
4.3.
Three-Point Distribution,
65
4.4.
Binomial Distribution,
66
4.5.
Poisson
Distribution,
70
4.6.
Exponential Distribution,
72
4.7.
Uniform Distribution,
78
4.8.
Logistic Distribution,
81
4.9.
Normal Distribution,
86
4.10.
Computer Simulation of Order Statistics,
95
Exercises,
97
5.
Moment Relations, Bounds, and Approximations
107
5.1.
Introduction,
107
5.2.
Basic Formulas,
108
5.3.
Some Identities and Recurrence Relations,
110
5.4.
Universal Bounds,
120
5.5.
Series Approximations,
128
Exercises,
132
6.
Characterizations Using Order Statistics
141
6.1.
Who Cares?,
141
6.2.
The Distribution of an Order Statistic Determines the Parent
Distribution,
142
6.3.
Characterizations Based on Moments of Order
Statistics,
143
6.4.
Characterizations Based on Distributional Relationships
among Order Statistics,
146
6.5.
Characterizations Involving Dependency Assumptions,
153
6.6.
Characterizations Involving Samples of Random Size,
155
Exercises,
157
7.
Order Statistics in Statistical Inference
159
7.1.
Introduction,
159
7.2.
Types of Order Statistics Data,
160
7.3.
Order Statistics and Sufficiency,
162
7.4.
Maximum-Likelihood Estimation,
167
CONTENTS
ХІ
7.5. Linear
Estimation
of Location and Scale Parameters,
171
7.6.
Prediction of Order Statistics,
180
7.7.
Distribution-Free Confidence and Tolerance Intervals,
183
7.8.
Goodness-of-Fit Tests,
186
7.9.
Other Applications,
189
Exercises,
194
8.
Asymptotic Theory
205
8.1.
Need and History,
205
8.2.
Exponential Order Statistics,
207
8.3.
Sample Maximum and Minimum,
208
8.4.
Other Extreme Order Statistics,
217
8.5.
Central and Intermediate Order Statistics,
223
8.6.
Linear Functions of Order Statistics,
227
Exercises,
234
9.
Record Values
241
9.1.
The Hottest July 4th On Record!,
241
9.2.
Definitions
and Preliminary Results on
Record Statistics,
242
9.3.
Distribution of the nth Upper Record,
243
9.4.
Distributions of Other Record Statistics,
245
9.5.
Record Range,
248
9.6.
Bounds on Mean Record Values,
249
9.7.
Record Values in Dependent Sequences,
251
9.8.
Records in Improving Populations,
252
Exercises,
254
Bibliography
259
Author Index
271
Subject Index
275 |
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| index_date | 2024-07-02T21:16:10Z |
| indexdate | 2024-07-09T21:17:18Z |
| institution | BVB |
| isbn | 9780898716481 |
| language | English |
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| physical | XXIII, 279 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | SIAM, Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Classics in applied mathematics |
| series2 | Classics in applied mathematics |
| spelling | Arnold, Barry C. 1939- Verfasser (DE-588)111442435 aut A first course in order statistics Barry C. Arnold ; N. Balakrishnan ; H. N. Nagaraja Unabridged republ. of the work 1. publ. 1992 Philadelphia SIAM, Society for Industrial and Applied Mathematics 2008 XXIII, 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in applied mathematics 54 Originally published: New York : Wiley, c1992 1992 Order statistics Ordnungsstatistik (DE-588)4212486-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Ordnungsstatistik (DE-588)4212486-4 s DE-604 Balakrishnan, Narayanaswamy 1956- Verfasser (DE-588)122214846 aut Nagaraja, Haikady N. 1954- Verfasser (DE-588)104268697 aut Reproduktion von New York : Wiley, 1992 0-471-57416-3 (DE-604)BV008735857 Classics in applied mathematics 54 (DE-604)BV008258410 54 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016563540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arnold, Barry C. 1939- Balakrishnan, Narayanaswamy 1956- Nagaraja, Haikady N. 1954- A first course in order statistics Classics in applied mathematics Order statistics Ordnungsstatistik (DE-588)4212486-4 gnd |
| subject_GND | (DE-588)4212486-4 (DE-588)4151278-9 |
| title | A first course in order statistics |
| title_auth | A first course in order statistics |
| title_exact_search | A first course in order statistics |
| title_exact_search_txtP | A first course in order statistics |
| title_full | A first course in order statistics Barry C. Arnold ; N. Balakrishnan ; H. N. Nagaraja |
| title_fullStr | A first course in order statistics Barry C. Arnold ; N. Balakrishnan ; H. N. Nagaraja |
| title_full_unstemmed | A first course in order statistics Barry C. Arnold ; N. Balakrishnan ; H. N. Nagaraja |
| title_short | A first course in order statistics |
| title_sort | a first course in order statistics |
| topic | Order statistics Ordnungsstatistik (DE-588)4212486-4 gnd |
| topic_facet | Order statistics Ordnungsstatistik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016563540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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