Holdings: Statistik und Wahrscheinlichkeitstheorie using R

Statistik und Wahrscheinlichkeitstheorie using R:

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Bibliographic Details
Main Author:	Gurker, Werner (Author)
Format:	Book
Language:	German
Published:	Wien TU-MV Media Verlag GmbH [2018]
Subjects:	Wahrscheinlichkeitstheorie Statistik R > Programm 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 Lehrbuch Einführung
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	viii, 467 Seiten Illustrationen 30 cm
ISBN:	9783903024793 3903024791

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Record in the Search Index

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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 BAYESSCHE 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 BAYESSCHE 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
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discipline	Informatik Mathematik Wirtschaftswissenschaften
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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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