Statistik und Wahrscheinlichkeitstheorie using R:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | German |
Veröffentlicht: |
Wien
TU-MV Media Verlag GmbH
[2018]
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
Beschreibung: | viii, 467 Seiten Illustrationen 30 cm |
ISBN: | 9783903024793 3903024791 |
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245 | 1 | 0 | |a Statistik und Wahrscheinlichkeitstheorie using R |c Werner Gurker |
264 | 1 | |a Wien |b TU-MV Media Verlag GmbH |c [2018] | |
300 | |a viii, 467 Seiten |b Illustrationen |c 30 cm | ||
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653 | |a Ass.Prof.i.R. Dipl.-Ing. Dr.techn. Werner Gurker Institut für Stochastik und Wirtschaftsmathematik Technische Universität Wien Wiedner Hauptstraße 8 – 10 | E105 A – 1040 Wien | ||
653 | |a TU wien Skripten grafisches Zentrum tuverlag | ||
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Datensatz im Suchindex
_version_ | 1804180062730190848 |
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adam_text | INHALTSVERZEICHNIS
1 DESKRIPTIVE UND EXPLORATIVE STATISTIK 1
1.1
GRUNDGESAMTHEIT....................................................................................................................
1
1.2 STICHPROBEN
..........................................................................................................................
2
1.3 MERKMALE
.............................................................................................................................
2
1.4
MESSNIVEAU.............................................................
!
............................................................
4
1.5 D A TE N M A
TRIX..........................................................................................................................
6
1.6 DISKRETE UNIVARIATE M E RKM A LE
.............................................................................................
7
1.6.1 H
AEUFIGKEITEN.............................................................................................................
7
1.6.2
KREISDIAGRAMM..........................................................................................................
8
1.6.3
BALKENDIAGRAMM.......................................................................................................
9
1.6.4 M
OSAIKPLOT................................................................................................................
9
1.6.5 PARETO-DIAGRAM M
....................................................................................................
10
1.7 STETIGE UNIVARIATE M ERKM
ALE.................................................................................................
13
1.7.1
ORDNUNGSSTATISTIKEN................................................................................................
13
1.7.2 EMPIRISCHE V
ERTEILUNGSFUNKTION.............................................................................
14
1.7.3 STEM
-AND-LEAF-PLOT................................................................................................
15
1.7.4 KLASSIERUNG
.............................................................................................................
16
1.7.5 H ISTO G RAM M
.............................................................................................................
18
1.7.6
KERNSCHAETZUNG..........................................................................................................
20
1.7.7 Q U A N TILE
....................................................................................................................
23
1.7.8 Q Q -P LO
T....................................................................................................................
26
1.7.9 BOXPLOT
....................................................................................................................
27
1.8
KENNZAHLEN.............................................................................................................................
29
1.8.1 M ITTE LW E
RT................................................................................................................
30
1.8.2 GEOMETRISCHES UND HARMONISCHES MITTEL
............................................................. 31
1.8.3 GETRIMMTER MITTELWERT
..........................................................................................
33
1.8.4 M
EDIAN.......................................................................................................................
34
1.8.5 V
ARIANZ........................................................................................................................
35
1.8.6 M A D
...........................................................................................................................
37
1.8.7 DATENZUSAMMENFASSUNG
..........................................................................................
38
1.8.8 M O D A LW E
RT.................................................................................................................
39
1.8.9 MOM
ENTE....................................................................................................................
41
1.8.10 S
CHIEFE........................................................................................................................
41
1.8.11 K U RTO S IS
....................................................................................................................
42
1.8.12 V ERTE ILUN G SFO RM
.......................................................................................................
43
1.9 MEHRDIMENSIONALE DATEN
....................................................................................................
44
1.9.1 S C A TTE RP LO TS
..............................................................................................................
46
1.9.2 KERNSCHAETZUNG
......................................................
46
1.9.3
KORRELATION.................................................................................................................
49
1.9.4 KLEINSTE Q U A D RA TE
....................................................................................................
56
AUFGABEN...........................................................................................................................................
60
2 WAHRSCHEINLICHKEIT 65
2.1 GESETZ DER GROSSEN Z A H LE N
....................................................................................................
65
2.2 M E RK M A LRA U M
........................................................................................................................
67
2.3 EREIGNISSE
..............................................................................................................................
69
2.4
BORELMENGEN...........................................................................................................................
71
2.5 WAHRSCHEINLICHKEITSMASSE
....................................................................................................
73
2.6 CHANCEN (O D D S
)....................................................................................................................
74
2.7 ENDLICHE W -R AE U M E
..............................................................................................................
76
2.8 GEOMETRISCHE
WAHRSCHEINLICHKEITEN....................................................................................
77
2.9 ADDITIONSTHEOREM
.................................................................................................................
78
2.10 BEDINGTE
WAHRSCHEINLICHKEIT.................................................................................................
81
2.11 MULTIPLIKATIONSTHEOREM
.......................................................................................................
83
2.12 VOLLSTAENDIGE W
AHRSCHEINLICHKEIT..........................................................................................
84
2.13 BAYES*SCHE F O RM E
L.................................................................................................................
86
2.14 UNABHAENGIGKEIT ....
2.15 MEHRSTUFIGE E XP E RIM E N TE
...................................................................................................
91
2.16 B
EISPIELE................................................................................................................................
94
AUFGABEN..............................................................................................................................................102
ANHANG: ABZAEHLENDE K O M B IN A TO
RIK.................................................................................................107
3 STOCHASTISCHE GROESSEN UND VERTEILUNGEN 111
3.1 STOCHASTISCHE G ROE SS E N
..............................................................................................................111
3.2 VERTEILUNGSFUNKTION
.................................................................................................................113
3.2.1 DISKRETE V ERTE ILUN G EN
.................................................................................................118
3.2.2 STETIGE
VERTEILUNGEN....................................................................................................
118
3.2.3 GEMISCHTE V
ERTEILUNGEN..............................................................................................122
3.3 TRANSFORMATIONEN
....................................................................................................................
125
3.3.1 TRANSFORMATIONEN DISKRETER S G N
.................................................................................126
3.3.2 TRANSFORMATIONEN STETIGER SGN
.................................................................................127
3.4 ERWARTUNGSWERT
.......................................................................................................................
132
3.5 V
ARIANZ.......................................................................................................................................
136
3.6 S IM U LA TIO N
.................................................................................................................................139
AUFGABEN..............................................................................................................................................143
4 SPEZIELLE VERTEILUNGEN 147
4.1 DISKRETE V E RTE ILU N G E N
..............................................................................................................147
4.1.1 DISKRETE UNIFORME V E RTE ILU N G
....................................................................................147
4.1.2
BERNOULLI-VERTEILUNG....................................................................................................149
4.1.3
BINOMIALVERTEILUNG.......................................................................................................
150
4.1.4 NEGATIVE
BINOMIALVERTEILUNG.......................................................................................
152
4.1.5 GEOMETRISCHE
VERTEILUNG..............................................................................................154
4.1.6 HYPERGEOMETRISCHE V
ERTEILUNG....................................................................................157
4.1.7 POISSON-VERTEILUNG
....................................................................................................159
4.2 STETIGE
VERTEILUNGEN...................................................................................................................162
4.2.1 STETIGE UNIFORME V E RTE ILU N G
........................................................................................163
4.2.2
EXPONENTIALVERTEILUNG.................................................................................................
164
4.2.3 GAMMA- UND
CHIQUADRATVERTEILUNG...........................................................................168
4.2.4 NORMALVERTEILUNG
........................................................................................................170
4.2.5 F -V E RTEILU NG
..................................................................................................................174
4.2.6 T-V E RTE ILU N G
..................................................................................................................176
4.2.7
BETAVERTEILUNG..............................................................................................................
177
AUFGABEN...............................................................................................................................................179
ANHANG: R-FUNKTIONEN
.....................................................................................................................182
5 MULTIVARIATE VERTEILUNGEN 185
5.1 BIVARIATE V
ERTEILUNGEN..............................................................................................................
185
5.1.1 DISKRETE STOCHASTISCHE
VEKTOREN.................................................................................
186
5.1.2 STETIGE STOCHASTISCHE V E K TO RE N
.................................................................................
188
5.1.3 E RW A RTU NG SW E
RT...........................................................................................................
191
5.1.4 BEDINGTE
VERTEILUNGEN.................................................................................................
192
5.2 K
ORRELATION..................................................................................................................................197
5.3 UNABHAENGIGKEIT
........................................................................................................................200
5.4 MEHRDIMENSIONALE ERW
EITERUNGEN...........................................................................................203
5.4.1 VARIANZ-KOVARIANZMATRIX
...........................................................................................206
5.5 TRANSFORMATIONEN
....................................................................................................................
207
5.6 SPEZIELLE MULTIVARIATE V E RTE ILU N G E N
.......................................................................................
213
5.6.1 M ULTINOM
IALVERTEILUNG.................................................................................................
213
5.6.2 POLYHYPERGEOMETRISCHE
VERTEILUNG..............................................................................215
5.6.3 MULTIVARIATE
NORMALVERTEILUNG....................................................................................
217
AUFGABEN..............................................................................................................................................
223
ANHANG: METHODE DER ANNAHME UND
VERWERFUNG...........................................................................227
6 FOLGEN VON STOCHASTISCHEN GROESSEN 233
6.1 LINEARE FUNKTIONEN
.................................................................................................................233
6.2
FALTUNG.......................................................................................................................................
236
6.2.1 DISKRETE F A LTU N G
..........................................................................................................
236
6.2.2 STETIGE FALTUNG
..........................................................................................................
238
6.2.3
ADDITIONSTHEOREME.......................................................................................................239
6.3 KONVERGENZ
..............................................................................................................................241
6.3.1
UNGLEICHUNGEN.............................................................................................................
242
6.3.2 GESETZ DER GROSSEN Z A H LE N
..........................................................................................
244
6.3.3 ZENTRALER GRENZVERTEILUNGSSATZ
................................................................................
246
6.3.4 NORM ALAPPROXIM
ATION.................................................................................................251
AUFGABEN..............................................................................................................................................253
7 SCHLIESSENDE STATISTIK 257
7.1 GRUNDBEGRIFFE
..........................................................................................................................
257
7.2 S C H AE TZ E
R....................................................................................................................................259
7.2.1 EMPIRISCHE V ERTEILUNGSFUNKTION
................................................................................
259
7.2.2
MOMENTENSCHAETZER.......................................................................................................
261
7.2.3 MAXIMUM LIKELIHOOD
.................................................................................................263
7.2.4 GUETEKRITERIEN FUER
SCHAETZER..........................................................................................
269
7.3
KONFIDENZINTERVALLE....................................................................................................................276
7.3.1 P IVO TM ETH OD E
.............................................................................................................
276
7.3.2 APPROXIMATIVES KONFIDENZINTERVALL FUER DEN M ITTE LW E R
T........................................ 279
7.3.3 NORMALVERTEILUNG (EINE S
TICHPROBE)..........................................................................
280
7.3.4 NORMALVERTEILUNG (ZWEI UA. S TICHP RO B EN )
................................................................
281
7.3.5 NORMALVERTEILUNG (VERBUNDENE STICHPROBEN)
..........................................................283
7.3.6
EXPONENTIALVERTEILUNG.................................................................................................285
7.3.7
BERNOULLI-VERTEILUNG....................................................................................................286
7.3.8 POISSON-VERTEILUNG
....................................................................................................288
7.3.9 RESAMPLING UND B O O TSTRA P P IN G
................................................................................
290
7.4 STATISTISCHE T E S T S
......................................................................................................................293
7.4.1
PARAMETERTESTS..............................................................................................................293
7.4.2 P-W E RT
........................................................................................................................298
7.4.3 BEZIEHUNG ZWISCHEN TESTS UND KONFIDENZINTERVALLEN
.............................................
300
7.4.4 TESTS FUER DEN MITTELWERT EINER NORMALVERTEILUNG (VARIANZ B E K A N
N T)
.....................
301
7.4.5 TESTS FUER DEN MITTELWERT EINER NORMALVERTEILUNG (VARIANZ
UNBEKANNT)
..................
302
7.4.6 TESTS FUER DIE VARIANZ EINER NORM ALVERTEILUNG
..........................................................
305
7.4.7 TESTS FUER EINEN A N T E
IL.................................................................................................
306
7.4.8 TESTS FUER DIE MITTELWERTE VON ZWEI NORMALVERTEILUNGEN
..........................................
310
7.4.9 TESTS FUER DIE VARIANZEN VON ZWEI NORMALVERTEILUNGEN
.............................................
312
7.4.10 TESTS FUER DEN
KORRELATIONSKOEFFIZIENTEN....................................................................314
7.4.11 NORMAL-QQ-PLOT
........................................................................................................315
7.4.12 CHIQUADRAT-ANPASSUNGSTESTS
................................................................... 318
AUFGABEN..............................................................................................................................................
323
ANHANG: N O RM A L-W -N E TZ
.................................................................................................................
330
8 BAYES-STATISTIK 331
8.1 A-PRIORI- UND A
-POSTERIORI-VERTEILUNG....................................................................................
331
8.2 KONJUGIERTE VERTEILUNGSFAM
ILIEN..............................................................................................334
8.3 BAYES-SCHAETZER
........................................................................................................................339
8.4 BAYES*SCHE
INTERVALLSCHAETZER....................................................................................................
341
8.5 B AYES-T
ESTS..............................................................................................................................
342
AUFGABEN..............................................................................................................................................
345
9 REGRESSIONSANALYSE 347
9.1 EINFACHE LINEARE R
EGRESSION.....................................................................................................
347
9.1.1
PARAMETERSCHAETZUNG....................................................................................................
350
9.1.2 VERTEILUNG DER KOEFFIZIENTEN
.......................................................................................
353
9.1.3
VARIANZZERLEGUNG..........................................................................................................
354
9.1.4
BESTIMMTHEITSMASS.......................................................................................................
356
9.1.5 ANOVA-TAFEL UND F - T E S T
.........................................................................................357
9.1.6 KONFIDENZINTERVALLE UND T-T E S TS
..................................................................................
360
9.1.7
RESIDUALANALYSE..........................................................................................................
364
9.1.8 AUSREISSER UND H
EBELPUNKTE.......................................................................................
366
9.1.9
MATRIXSCHREIBWEISE.......................................................................................................
370
9.2 MULTIPLE LINEARE REGRESSION
....................................................................................................
372
9.2.1
PARAMETERSCHAETZUNG....................................................................................................373
9.2.2 ANOVA-TAFEL UND F - T E S T
.........................................................................................375
9.2.3 KONFIDENZINTERVALLE UND T-T E S TS
...................................................................................377
9.2.4 B
EISPIELE.......................................................................................................................
378
AUFGABEN..............................................................................................................................................387
10 ERGAENZUNGEN 391
10.1 E N TRO P IE
....................................................................................................................................391
10.1.1 UE
BERRASCHUNG.............................................................................................................
391
10.1.2 E N TRO P IE
.......................................................................................................................
393
10.1.3 C O D IE RU N G
................................................................................................................
395
10.2 BAYES SCHE NETZE
....................................................................................................................400
10.3 M A RK O W -K E TTE N
.......................................................................................................................
407
10.4
ZAEHLPROZESSE.............................................................................................................................
417
10.4.1
BERNOULLI-PROZESSE.......................................................................................................
417
10.4.2
POISSON-PROZESSE.......................................................................................................
421
10.5 W
ARTESCHLANGEN.......................................................................................................................
428
10.5.1
HAUPTBESTANDTEILE.......................................................................................................
429
10.5.2 M /M /L- S Y S TE M E
.......................................................................................................
432
10.5.3 M /M /L/A T -S Y S TE M E
.................................................................................................439
10.5.4 M /M /& -S Y S TE M E
.......................................................................................................
440
AUFGABEN..............................................................................................................................................
443
ANHANG: WALD*SCHE IDENTITAET
...........................................................................................................447
TABELLEN 449
ANTWORTEN ZU DEN AUFGABEN 453
LITERATUR 457
INDEX 459
|
any_adam_object | 1 |
author | Gurker, Werner |
author_GND | (DE-588)1173740651 |
author_facet | Gurker, Werner |
author_role | aut |
author_sort | Gurker, Werner |
author_variant | w g wg |
building | Verbundindex |
bvnumber | BV045899797 |
classification_rvk | QH 231 SK 800 ST 601 |
ctrlnum | (DE-599)DNB1166585441 |
dewey-full | 519.2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2 |
dewey-search | 519.2 |
dewey-sort | 3519.2 |
dewey-tens | 510 - Mathematics |
discipline | Informatik Mathematik Wirtschaftswissenschaften |
format | Book |
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genre | (DE-588)4123623-3 Lehrbuch gnd-content (DE-588)4151278-9 Einführung gnd-content |
genre_facet | Lehrbuch Einführung |
id | DE-604.BV045899797 |
illustrated | Illustrated |
indexdate | 2024-07-10T08:29:47Z |
institution | BVB |
isbn | 9783903024793 3903024791 |
language | German |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031282641 |
open_access_boolean | |
owner | DE-703 |
owner_facet | DE-703 |
physical | viii, 467 Seiten Illustrationen 30 cm |
publishDate | 2018 |
publishDateSearch | 2018 |
publishDateSort | 2018 |
publisher | TU-MV Media Verlag GmbH |
record_format | marc |
spelling | Gurker, Werner Verfasser (DE-588)1173740651 aut Statistik und Wahrscheinlichkeitstheorie using R Werner Gurker Wien TU-MV Media Verlag GmbH [2018] viii, 467 Seiten Illustrationen 30 cm txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Fachhochschul-/Hochschulausbildung Junge Erwachsene Ass.Prof.i.R. Dipl.-Ing. Dr.techn. Werner Gurker Institut für Stochastik und Wirtschaftsmathematik Technische Universität Wien Wiedner Hauptstraße 8 – 10 | E105 A – 1040 Wien TU wien Skripten grafisches Zentrum tuverlag Werner Gurker (DE-588)4123623-3 Lehrbuch gnd-content (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s R Programm (DE-588)4705956-4 s DE-604 B:DE-101 application/pdf http://d-nb.info/1166585441/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031282641&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Gurker, Werner Statistik und Wahrscheinlichkeitstheorie using R Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd R Programm (DE-588)4705956-4 gnd |
subject_GND | (DE-588)4079013-7 (DE-588)4056995-0 (DE-588)4705956-4 (DE-588)4123623-3 (DE-588)4151278-9 |
title | Statistik und Wahrscheinlichkeitstheorie using R |
title_auth | Statistik und Wahrscheinlichkeitstheorie using R |
title_exact_search | Statistik und Wahrscheinlichkeitstheorie using R |
title_full | Statistik und Wahrscheinlichkeitstheorie using R Werner Gurker |
title_fullStr | Statistik und Wahrscheinlichkeitstheorie using R Werner Gurker |
title_full_unstemmed | Statistik und Wahrscheinlichkeitstheorie using R Werner Gurker |
title_short | Statistik und Wahrscheinlichkeitstheorie using R |
title_sort | statistik und wahrscheinlichkeitstheorie using r |
topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd R Programm (DE-588)4705956-4 gnd |
topic_facet | Wahrscheinlichkeitstheorie Statistik R Programm Lehrbuch Einführung |
url | http://d-nb.info/1166585441/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031282641&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT gurkerwerner statistikundwahrscheinlichkeitstheorieusingr |
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Inhaltsverzeichnis