Statistics of the Boolean model for practitioners and mathematicians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1997
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Offenbar vergriffen | 23.4.2001 |
| Beschreibung: | VI, 162 S. Ill., graph. Darst. |
| ISBN: | 0471971022 |
Internformat
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| 100 | 1 | |a Molčanov, Il'ja S. |d 1962- |e Verfasser |0 (DE-588)1016701861 |4 aut | |
| 245 | 1 | 0 | |a Statistics of the Boolean model for practitioners and mathematicians |c Ilya Molchanov |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1997 | |
| 300 | |a VI, 162 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Offenbar vergriffen | 23.4.2001 | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007642291 | ||
Datensatz im Suchindex
| _version_ | 1804125882532495360 |
|---|---|
| adam_text | Contents
1 Introduction 1
2 The Boolean Model 5
2.1 Basic Notation 5
2.2 Point Patterns and Point Processes 6
2.3 Definition of the Boolean Model 9
2.4 Examples of Boolean Models 14
2.5 Characteristics and Important Parameters 17
2.6 Individual and Aggregate Parameters 25
3 Estimation of Aggregate Parameters 29
3.1 Area Fraction 29
3.2 Specific Convexity Number 33
3.3 Specific Boundary Length 39
3.4 Specific Connectivity Number 43
3.5 Set Valued Aggregate Parameters 49
4 Estimation of Functional Aggregate Parameters 57
4.1 Capacity Functional 57
4.2 Covariance 64
4.3 Contact Distribution Functions 65
4.4 Pair Correlation Functions 71
5 Estimation of Numerical Individual Parameters 77
5.1 Minimum Contrast Method 77
5.2 Method of Intensities 81
5.3 Tangent Points Method 83
5.4 Schmitt s Method 86
5.5 Other Methods 89
6 Estimation of Set Valued Individual Parameters 93
6.1 Mean Difference Body 93
vi CONTENTS
6.2 Convexification and the Mean Body 96
7 Individual Parameters: Distributions 101
7.1 Deterministic Grain 101
7.2 Distribution of the Radius of the Spherical Grain 104
7.3 Covering Probabilities 107
7.4 Finite Dimensional Distributions of the Support Function . . . Ill
8 Other Sampling Schemes 117
8.1 Parametric Models 117
8.2 Lower Dimensional Sections 119
8.3 Point Sampling 121
8.4 Spatial Censoring 123
8.5 Multiphased Boolean Models 124
8.6 Discrete Boolean Models 125
9 Testing the Boolean Model Assumption 127
9.1 Graphical Tests 127
9.2 Laslett s Transform 129
9.3 Heuristic Testing of the Convexity Assumption 131
10 An Example 133
10.1 Area Fraction and Covariance 133
10.2 Specific Boundary Length 134
10.3 Specific Convexity and Connectivity Numbers, and Related
Individual Parameters 135
10.4 Contact Distribution Functions and Minimum
Contrast Method 137
10.5 Set Valued Aggregate Parameters and the Mean
Difference Body 139
10.6 Pair Correlation Function and Covering Probabilities 141
10.7 Parametric Models 141
11 Concluding Remarks 145
References 147
Index 159
|
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| building | Verbundindex |
| bvnumber | BV011372707 |
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| ctrlnum | (OCoLC)634800813 (DE-599)BVBBV011372707 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011372707 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:08:37Z |
| institution | BVB |
| isbn | 0471971022 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007642291 |
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| physical | VI, 162 S. Ill., graph. Darst. |
| publishDate | 1997 |
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| publisher | Wiley |
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| spelling | Molčanov, Il'ja S. 1962- Verfasser (DE-588)1016701861 aut Statistics of the Boolean model for practitioners and mathematicians Ilya Molchanov Chichester [u.a.] Wiley 1997 VI, 162 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Offenbar vergriffen | 23.4.2001 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007642291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Molčanov, Il'ja S. 1962- Statistics of the Boolean model for practitioners and mathematicians |
| title | Statistics of the Boolean model for practitioners and mathematicians |
| title_auth | Statistics of the Boolean model for practitioners and mathematicians |
| title_exact_search | Statistics of the Boolean model for practitioners and mathematicians |
| title_full | Statistics of the Boolean model for practitioners and mathematicians Ilya Molchanov |
| title_fullStr | Statistics of the Boolean model for practitioners and mathematicians Ilya Molchanov |
| title_full_unstemmed | Statistics of the Boolean model for practitioners and mathematicians Ilya Molchanov |
| title_short | Statistics of the Boolean model for practitioners and mathematicians |
| title_sort | statistics of the boolean model for practitioners and mathematicians |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007642291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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