Probability theory and statistics with real world applications: univariate and multivariate models applications
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin
De Gruyter
[2024]
|
| Ausgabe: | 2nd, Revised and Extended Edition |
| Schriftenreihe: | De Gruyter Textbook
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035149092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 358 Seiten Illustrationen |
| ISBN: | 9783111332208 |
Internformat
MARC
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| 245 | 1 | 0 | |a Probability theory and statistics with real world applications |b univariate and multivariate models applications |c Peter Zörnig |
| 250 | |a 2nd, Revised and Extended Edition | ||
| 264 | 1 | |a Berlin |b De Gruyter |c [2024] | |
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| 653 | |a Univariate und multivariate Modelle | ||
| 653 | |a Wahrscheinlichkeitsmaße | ||
| 653 | |a Transformationen von Zufallsvariablen | ||
| 653 | |a Funktionen generieren | ||
| 653 | |a Bestellstatistik | ||
| 653 | |a Univariate and multivariate models | ||
| 653 | |a Probability measures | ||
| 653 | |a Transforms of random variables | ||
| 653 | |a Generating functions | ||
| 653 | |a Convergence of random variables | ||
| 653 | |a Order statistics | ||
| 653 | |a Statistical applications | ||
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Datensatz im Suchindex
| _version_ | 1823320652740820992 |
|---|---|
| adam_text |
Contents Acknowledgment — V Preface to the first edition — VII Preface to the second edition — IX 1 Mathematics revision — 1 1.1 Basic notions of sets----- 1 Exercises — 4 1.2 1.2.1 Basic concepts of combinatorics — 5 1.2.2 Specific permutations and a generalization —11 Exercises —14 1.3 Some special functions —15 Exercises —19 1.4 Integration of bidimensional functions----- 21 Exercises — 27 2 2.1 More about binomial coefficients — 7 Introduction to probability — 29 Mathematical models — 29 2.2 Further examples of random experiments — 29 2.3 Assigning probabilities to events — 31 2.4 Basic notions of probability----- 33 Exercises — 37 3 3.1 3.2 Finite sample spaces — 39 Equally likely outcomes----- 39 Variants of a random experiment — 44 Exercises — 47 4 Conditional probability and independence — 49 4.1 Conditional probability----- 49 4.2 Bayes’ theorem----- 53 4.3 Independent events----- 55 Exercises — 62 5 5.1 One-dimensional random variables — 67 The concept of a random variable — 67 5.2 Discrete random variables----- 68 5.3 The binomial distribution and extensions — 69
XII 5.4 5.5 — Contents Continuous random variables----- 72 Distribution and survival function----- 75 Exercises — 78 б Functions of random variables----- 82 6.1 Continuous random variables----- 82 6.2 Discrete random variables — 88 Exercises----- 90 7 Bidimensional random variables----- 92 7.1 Discrete random variables — 92 7.2 Continuous random variables----- 94 7.3 Marginal distributionsand independent variables — 97 7.4 Conditional distributions, distribution and survival functions —101 7.5 Functions of a random variable----- 105 Exercises —108 8 Characteristics of random variables —111 8.1 The expected value of a random variable —111 8.2 Expectation of a function of a random variable —113 8.3 Properties of the expected value —115 8.4 Variance, moments, and shape characteristics —117 8.5 Probability inequalities----- 123 8.6 Covariance and correlation —126 Exercises----- 130 9 Discrete probability models —133 9.1 The Poisson distribution----- 133 9.2 The Poisson process----- 135 9.3 The geometric distribution —137 9.4 The Pascal distribution----- 139 9.5 The hypergeometric distribution —141 9.6 The multinomial distribution----- 144 Exercises----- 145 10 Continuous probability models----- 148 10.1 The normal distribution----- 148 10.2 The exponential distribution----- 154 10.3 The gamma distribution----- 155 10.4 The chi-square distribution----- 157 10.5 The beta distribution —159 The multivariate normal distribution —160 10.6
Contents 10.7 A bivariate exponential distribution —166 Exercises —167 11 Generating functions in probability —170 11.1 The moment-generating function —170 11.2 Generation of moments------ 172 11.3 Reproductive properties —175 11.4 The probability-generating function—179 11.5 Generation of probabilities and factorial moments —181 Exercises —184 12 Construction of new distributions----- 186 12.1 A classical construction principle----- 186 12.2 Exponentiated generalized distribution —190 12.3 Mixture distributions------ 192 12.4 An extended distribution class------ 194 12.5 Transformations of a random variable —196 12.6 Functions of two variables —198 12.7 Slash distributions------199 Exercises — 200 13 Sums of many random variables — 203 13.1 13.2 The law of large numbers — 203 Normal approximation to the binomial distribution----- 204 13.3 The central limit theorem — 207 Exercises — 210 14 Samples and sampling distributions — 212 14.1 Samples and statistics------212 14.2 Order statistics----- 214 14.3 Sampling in simulation and deterministic applications — 219 Exercises — 225 15 Estimation of parameters----- 228 15.1 Criteria for estimators----- 228 15.2 Maximum likelihood estimation----- 232 15.3 15.4 Method of moments----- 238 15.5 Confidence intervals----- 249 15.6 Student’s t-distribution----- 253 Linear regression----- 242 Exercises — 255 — XIII
XIV — Contents 16 Hypothesis tests----- 259 16.1 Basic concepts and tests----- 259 16.2 OC-function, power function and p-value — 263 16.3 Tests for the mean of a normal distribution with unknown variance — 268 16.4 Tests for the variance of a normal distribution — 269 16.5 Comparing the means of two normal distributions — 270 16.6 Comparing the variances of two normal distributions — 274 16.7 Chi-square goodness-of-fit test----- 276 16.8 Contingency table chi-square test — 279 Exercises — 281 17 Exploratory data analysis — 284 17.1 Introduction----- 284 17.2 Summary measures — 287 17.3 Bidimensional analyses — 298 Exercises — 306 Appendix----- 311 Solutions to exercises — 311 Table of distributions----- 344 Standard normal distribution----- 347 Student’s t-distribution----- 348 Chi-square distribution----- 350 References — 353 Index----- 355 |
| any_adam_object | 1 |
| author | Zörnig, Peter 1955- |
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| building | Verbundindex |
| bvnumber | BV049808656 |
| classification_rvk | QH 170 |
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| discipline | Wirtschaftswissenschaften |
| edition | 2nd, Revised and Extended Edition |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-02-06T15:01:16Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783111332208 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035149092 |
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| physical | XIV, 358 Seiten Illustrationen |
| publishDate | 2024 |
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| spelling | Zörnig, Peter 1955- Verfasser (DE-588)1047567814 aut Probability theory and statistics with real world applications univariate and multivariate models applications Peter Zörnig 2nd, Revised and Extended Edition Berlin De Gruyter [2024] XIV, 358 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier De Gruyter Textbook Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Univariate und multivariate Modelle Wahrscheinlichkeitsmaße Transformationen von Zufallsvariablen Funktionen generieren Bestellstatistik Univariate and multivariate models Probability measures Transforms of random variables Generating functions Convergence of random variables Order statistics Statistical applications Statistik (DE-588)4056995-0 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-133227-7 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-133232-1 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035149092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zörnig, Peter 1955- Probability theory and statistics with real world applications univariate and multivariate models applications Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4056995-0 |
| title | Probability theory and statistics with real world applications univariate and multivariate models applications |
| title_auth | Probability theory and statistics with real world applications univariate and multivariate models applications |
| title_exact_search | Probability theory and statistics with real world applications univariate and multivariate models applications |
| title_full | Probability theory and statistics with real world applications univariate and multivariate models applications Peter Zörnig |
| title_fullStr | Probability theory and statistics with real world applications univariate and multivariate models applications Peter Zörnig |
| title_full_unstemmed | Probability theory and statistics with real world applications univariate and multivariate models applications Peter Zörnig |
| title_short | Probability theory and statistics with real world applications |
| title_sort | probability theory and statistics with real world applications univariate and multivariate models applications |
| title_sub | univariate and multivariate models applications |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035149092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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