Probability and statistics: a course for physicists and engineers
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2018]
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| Series: | De Gruyter textbook
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| Subjects: | |
| Online Access: | Volltext Volltext Volltext Inhaltsverzeichnis |
| Item Description: | Erscheint auch als Open Access bei De Gruyter |
| Physical Description: | XXII, 582 Seiten Illustrationen |
| ISBN: | 9783110562538 |
| DOI: | 10.1515/9783110562545 |
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MARC
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| 100 | 1 | |a Mathai, Arakaparampil M. |d 1935- |e Verfasser |0 (DE-588)141316241 |4 aut | |
| 245 | 1 | 0 | |a Probability and statistics |b a course for physicists and engineers |c Arak M. Mathai and Hans J. Haubold |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a XXII, 582 Seiten |b Illustrationen | ||
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| 700 | 1 | |a Haubold, Hans J. |d 1951- |e Verfasser |0 (DE-588)136316190 |4 aut | |
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Record in the Search Index
| DE-BY-FWS_katkey | 680656 |
|---|---|
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| adam_text |
CONTENTS
PREFACE * IX
ACKNOWLEDGEMENT * XI
LIST OF TABLES * XIX
LIST OF SYMBOLS* XXI
1 RANDOM PHENOMENA * 1
1.1 INTRODUCTION * 1
1.1.1 WAITING TIME * 1
1.1.2 RANDOM EVENTS * 2
1.2 A RANDOM EXPERIMENT * 7
1.3 VENN DIAGRAMS * 14
1.4 PROBABILITY OR CHANCE OF OCCURRENCE OF A RANDOM EVENT *
1.4.1 POSTULATES FOR PROBABILITY * 18
1.5 HOW TO ASSIGN PROBABILITIES TO INDIVIDUAL EVENTS? * 22
1.5.1 BUFFON*S *CLEAN TILE PROBLEM* * 29
2 PROBABILITY * 33
2.1 INTRODUCTION * 33
2.2 PERMUTATIONS * 33
2.3 COMBINATIONS * 37
2.4 SUM X AND PRODUCT FL NOTATION * 41
2.4.1 THE PRODUCT NOTATION OR PI NOTATION * 45
2.5 CONDITIONAL PROBABILITIES * 48
2.5.1 THE TOTAL PROBABILITY LAW * 53
2.5.2 BAYES* RULE * 55
2.5.3 ENTROPY * 57
3 RANDOM VARIABLES * 61
3.1 INTRODUCTION * 61
3.2 AXIOMS FOR PROBABILITY/DENSITY FUNCTION AND DISTRIBUTION
FUNCTIONS * 66
3.2.1 AXIOMS FOR A DISTRIBUTION FUNCTION * 72
3.2.2 MIXED CASES * 72
3.3 SOME COMMONLY USED SERIES * 76
3.3.1 EXPONENTIAL SERIES * 76
3.3.2 LOGARITHMIC SERIES
-----
76
3.3.3 BINOMIAL SERIES * 77
3.3.4 TRIGONOMETRIC SERIES
-----
78
3.3.5 A NOTE ON LOGARITHMS * 78
4 EXPECTED VALUES * 83
4.1 INTRODUCTION
----
83
4.2 EXPECTED VALUES * 83
4.2.1 MEASURES OF CENTRAL TENDENCY * 88
4.2.2 MEASURES OF SCATTER OR DISPERSION * 91
4.2.3 SOME PROPERTIES OF VARIANCE * 91
4.3 HIGHER MOMENTS
----
95
4.3.1 MOMENT GENERATING FUNCTION * 100
4.3.2 MOMENTS AND MELLIN TRANSFORMS * 102
4.3.3 UNIQUENESS AND THE MOMENT PROBLEM * 104
5 COMMONLY USED DISCRETE DISTRIBUTIONS * 107
5.1 INTRODUCTION * 107
5.2 BERNOULLI PROBABILITY LAW
----
107
5.3 BINOMIAL PROBABILITY LAW
----
109
5.4 GEOMETRIC PROBABILITY LAW * 111
5.5 NEGATIVE BINOMIAL PROBABILITY LAW * 113
5.6 POISSON PROBABILITY LAW * 117
5.6.1 POISSON PROBABILITY LAW FROM A PROCESS * 121
5.7 DISCRETE HYPERGEOMETRIC PROBABILITY LAW * 123
5.8 OTHER COMMONLY USED DISCRETE DISTRIBUTIONS * 125
6 COMMONLY USED DENSITY FUNCTIONS * 133
6.1 INTRODUCTION
----
133
6.2 RECTANGULAR OR UNIFORM DENSITY * 133
6.3 A TWO-PARAMETER GAMMA DENSITY * 136
6.3.1 EXPONENTIAL DENSITY * 139
6.3.2 CHI-SQUARE DENSITY * 139
6.4 GENERALIZED GAMMA DENSITY
----
141
6.4.1 WEIBULL DENSITY * 142
6.5 BETA DENSITY * 143
6.6 LAPLACE DENSITY * 146
6.7 GAUSSIAN DENSITY OR NORMAL DENSITY * 147
6.7.1 MOMENT GENERATING FUNCTION OF THE NORMAL DENSITY *
6.8 TRANSFORMATION OF VARIABLES
----
153
6.9 A NOTE ON SKEWNESS AND KURTOSIS * 159
6.10 MATHAI*S PATHWAY MODEL
----
161
6.10.1 LOGISTIC MODEL
----
162
6.11
SOME MORE COMMONLY USED DENSITY FUNCTIONS
----
163
7
7.1
7.2
7.2.1
7.3
7.4
7.4.1
7.4.2
7.4.3
7.4.4
7.5
7.5.1
7.5.2
7.6
7.7
8
8.1
8.2
8
.
2.1
8
.
2.2
8.3
8.3.1
8.3.2
8.4
8.4.1
8.5
9
9.1
9.2
9.3
9.4
10
10.1
10.2
10.3
10.4
JOINT DISTRIBUTIONS
----
171
INTRODUCTION
----
171
MARGINAL AND CONDITIONAL PROBABILITY/DENSITY FUNCTIONS
----
176
GEOMETRICAL INTERPRETATIONS OF MARGINAL AND CONDITIONAL
DISTRIBUTIONS
----
179
STATISTICAL INDEPENDENCE OF RANDOM VARIABLES * 182
EXPECTED VALUE
----
185
SOME PROPERTIES OF EXPECTED VALUES * 189
JOINT MOMENT GENERATING FUNCTION * 191
LINEAR FUNCTIONS OF RANDOM VARIABLES * 195
SOME BASIC PROPERTIES OF THE CORRELATION COEFFICIENT
----
199
CONDITIONAL EXPECTATIONS
----
201
CONDITIONAL EXPECTATION AND PREDICTION PROBLEM
----
204
REGRESSION
----
206
BAYESIAN PROCEDURE
----
207
TRANSFORMATION OF VARIABLES
----
211
SOME MULTIVARIATE DISTRIBUTIONS * 221
INTRODUCTION
----
221
SOME MULTIVARIATE DISCRETE DISTRIBUTIONS
----
221
MULTINOMIAL PROBABILITY LAW
----
221
THE MULTIVARIATE HYPERGEOMETRIC PROBABILITY LAW
----
224
SOME MULTIVARIATE DENSITIES
----
227
TYPE-1 DIRICHLET DENSITY
----
227
TYPE-2 DIRICHLET DENSITY
----
230
MULTIVARIATE NORMAL OR GAUSSIAN DENSITY
----
233
MATRIX-VARIATE NORMAL OR GAUSSIAN DENSITY
----
242
MATRIX-VARIATE GAMMA DENSITY
----
243
COLLECTION OF RANDOM VARIABLES * 249
INTRODUCTION
----
249
LAWS OF LARGE NUMBERS * 252
CENTRAL LIMIT THEOREMS
----
253
COLLECTION OF DEPENDENT VARIABLES
----
257
SAMPLING DISTRIBUTIONS * 259
INTRODUCTION
----
259
SAMPLING DISTRIBUTIONS
----
262
SAMPLING DISTRIBUTIONS WHEN THE POPULATION IS NORMAL
----
272
STUDENT-F AND
F
DISTRIBUTIONS * 277
10.5 LINEAR FORMS AND QUADRATIC FORMS * 284
10.6 ORDER STATISTICS * 291
10.6.1 DENSITY OF THE SMALLEST ORDER STATISTIC X*:1 * 293
10.6.2 DENSITY OF THE LARGEST ORDER STATISTIC XN.* * 293
10.6.3 THE DENSITY OF THE R-TH ORDER STATISTIC
X*.R
* 294
10.6.4 JOINT DENSITY OF THE R-TH AND S-TH ORDER STATISTICS
XN:R
ANDX*.S * 298
11 ESTIMATION * 303
11.1 INTRODUCTION * 303
11.2 PARAMETRIC ESTIMATION * 305
11.3 METHODS OF ESTIMATION * 320
11.3.1 THE METHOD OF MOMENTS * 321
11.3.2 THE METHOD OF MAXIMUM LIKELIHOOD * 323
11.3.3 METHOD OF MINIMUM PEARSON*SX2 STATISTIC OR MINIMUM CHI-SQUARE
METHOD
----
329
11.3.4 MINIMUM DISPERSION METHOD * 330
11.3.5 SOME GENERAL PROPERTIES OF POINT ESTIMATORS * 332
11.4 POINT ESTIMATION IN THE CONDITIONAL SPACE * 337
11.4.1 BAYES* ESTI MATES * 337
11.4.2 ESTIMATION IN THE CONDITIONAL SPACE: MODEL BUILDING * 340
11.4.3 SOME PROPERTIES OF ESTIMATORS * 342
11.4.4 SOME LARGE SAMPLE PROPERTIES OF MAXIMUM LIKELIHOOD
ESTIMATORS * 344
11.5 DENSITY ESTIMATION * 349
11.5.1 UNIQUE DETERMINATION OF THE DENSITY/PROBABILITY FUNCTION * 349
11.5.2 ESTIMATION OF DENSITIES * 350
12 INTERVAL ESTIMATION * 355
12.1 INTRODUCTION * 355
12.2 INTERVAL ESTIMATION PROBLEMS * 355
12.3 CONFIDENCE INTERVAL FOR PARAMETERS IN AN EXPONENTIAL POPULATION *
358
12.4 CONFIDENCE INTERVAL FOR THE PARAMETERS IN A UNIFORM DENSITY * 360
12.5 CONFIDENCE INTERVALS IN DISCRETE DISTRIBUTIONS * 361
12.5.1 CONFIDENCE INTERVAL FOR THE BERNOULLI PARAMETER
P
* 362
12.6 CONFIDENCE INTERVALS FOR PARAMETERS IN
N(P,O2)
* 365
12.6.1 CONFIDENCE INTERVALS FOR
P
* 366
12.6.2 CONFIDENCE INTERVALS FOR
A2
IN
N(P,O2)
* 369
12.7 CONFIDENCE INTERVALS FOR LINEAR FUNCTIONS OF MEAN VALUES * 372
12.7.1 CONFIDENCE INTERVALS FOR MEAN VALUES WHEN THE VARIABLES ARE
DEPENDENT * 373
12.7.2 CONFIDENCE INTERVALS FOR LINEAR FUNCTIONS OF MEAN VALUES WHEN
THERE IS
STATISTICAL INDEPENDENCE * 375
12.7.3
CONFIDENCE INTERVALS FOR THE RATIO OF VARIANCES * 377
13 TESTS OF STATISTICAL HYPOTHESES * 381
13.1 INTRODUCTION * 381
13.2 TESTING A PARAMETRIC STATISTICAL HYPOTHESIS * 382
13.2.1 THE LIKELIHOOD RATIO CRITERION OR THE ^-CRITERION * 391
13.3 TESTING HYPOTHESES ON THE PARAMETERS OF A NORMAL POPULATION
N(P,A2)
* 395
13.3.1 TESTING HYPOTHESES ON
P
IN
N(P,O2)
WHEN
A2
IS KNOWN * 395
13.3.2 TESTS OF HYPOTHESES ON
P
IN
N(P,O2)
WHEN
A2
IS UNKNOWN * 396
13.3.3 TESTING HYPOTHESES ON
A2
IN A
N(P,O2)
* 399
13.4 TESTING HYPOTHESES IN BIVARIATE NORMAL POPULATION * 401
13.5 TESTING HYPOTHESES ON THE PARAMETERS OF INDEPENDENT NORMAL
POPULATIONS * 404
13.6 APPROXIMATIONS WHEN THE POPULATIONS ARE NORMAL * 408
13.6.1 STUDENT-F APPROXIMATION TO NORMAL * 408
13.6.2 APPROXIMATIONS BASED ON THE CENTRAL LIMIT THEOREM * 409
13.7 TESTING HYPOTHESES IN BINOMIAL, POISSON AND EXPONENTIAL
POPULATIONS * 411
13.7.1 HYPOTHESES ON
P,
THE BERNOULLI PARAMETER * 411
13.7.2 HYPOTHESES ON A POISSON PARAMETER * 413
13.7.3 HYPOTHESES IN AN EXPONENTIAL POPULATION * 414
13.8 SOME HYPOTHESES ON MULTIVARIATE NORMAL * 416
13.8.1 TESTING THE HYPOTHESIS OF INDEPENDENCE * 418
13.9 SOME NON-PARAMETRIC TESTS * 419
13.9.1 LACK-OF-FIT OR GOODNESS-OF-FIT TESTS * 420
13.9.2 TEST FOR NO ASSOCIATION IN A CONTINGENCY TABLE * 425
13.9.3 KOLMOGOROV-SMIRNOV STATISTIC
DN
-----
428
13.9.4 THE SIGN TEST * 430
13.9.5 THE RANKTEST
----
431
13.9.6 THE RUN TE S T
----
433
14 MODEL BUILDING AND REGRESSION * 437
14.1 INTRODUCTION
----
437
14.2 NON-DETERMINISTIC MODELS * 437
14.2.1 RANDOM WALK MODEL * 438
14.2.2 BRANCHING PROCESS MODEL
----
439
14.2.3 BIRTH AND DEATH PROCESS MODEL * 440
14.2.4 TIME SERIES MODELS
----
440
14.3 REGRESSION TYPE MODELS * 440
14.3.1 MINIMIZATION OF DISTANCE MEASURES * 441
14.3.2 MINIMUM MEAN SQUARE PREDICTION * 442
14.3.3 REGRESSION ON SEVERAL VARIABLES * 447
14.4 LINEAR REGRESSION * 450
14.4.1 CORRELATION BETWEEN
XX
AND ITS BEST LINEAR PREDICTOR * 457
14.5 MULTIPLE CORRELATION COEFFICIENT P1(2. *) * 459
14.5.1 SOME PROPERTIES OF THE MULTIPLE CORRELATION COEFFICIENT * 459
14.6 REGRESSION ANALYSIS VERSUS CORRELATION ANALYSIS * 466
14.6.1 MULTIPLE CORRELATION RATIO * 466
14.6.2 MULTIPLE CORRELATION AS A FUNCTION OF THE NUMBER OF REGRESSED
VARIABLES * 468
14.7 ESTIMATION OF THE REGRESSION FUNCTION * 475
14.7.1 ESTIMATION OF LINEAR REGRESSION OFY ON X * 476
14.7.2 INFERENCE ON THE PARAMETERS OF A SIMPLE LINEAR MODEL * 481
14.7.3 LINEAR REGRESSION OFY ONXA,.
,XK
* 484
14.7.4 GENERAL LINEAR MODEL * 489
15 DESIGN OF EXPERIMENTS AND ANALYSIS OF VARIANCE * 493
15.1 INTRODUCTION * 493
15.2 FULLY RANDOMIZED EXPERIMENTS * 494
15.2.1 ONE-WAY CLASSIFICATION MODEL AS A GENERAL LINEAR MODEL * 498
15.2.2 ANALYSIS OF VARIANCE TABLE OR ANOVA TABLE * 499
15.2.3 ANALYSIS OF INDIVIDUAL DIFFERENCES * 501
15.3 RANDOMIZED BLOCK DESIGN AND TWO-WAY CLASSIFICATIONS * 503
15.3.1 TWO-WAY CLASSIFICATION MODEL WITHOUT INTERACTION * 505
15.3.2 TWO-WAY CLASSIFICATION MODEL WITH INTERACTION * 510
15.4 LATIN SQUARE DESIGNS * 516
15.5 SOME OTHER DESIGNS * 521
15.5.1 FACTORIAL DESIGNS * 521
15.5.2 INCOMPLETE BLOCK DESIGNS * 522
15.5.3 RESPONSE SURFACE ANALYSIS * 522
15.5.4 RANDOM EFFECT MODELS * 522
16 QUESTIONS AND ANSWERS * 525
16.1 QUESTIONS AND ANSWERS ON PROBABILITY AND RANDOM VARIABLES * 525
16.2 QUESTIONS AND ANSWERS ON MODEL BUILDING * 539
16.3 QUESTIONS AND ANSWERS ON TESTS OF HYPOTHESES * 549
TABLES OF PERCENTAGE POINTS * 559
REFERENCES * 577
INDEX * 579 |
| any_adam_object | 1 |
| author | Mathai, Arakaparampil M. 1935- Haubold, Hans J. 1951- |
| author_GND | (DE-588)141316241 (DE-588)136316190 |
| author_facet | Mathai, Arakaparampil M. 1935- Haubold, Hans J. 1951- |
| author_role | aut aut |
| author_sort | Mathai, Arakaparampil M. 1935- |
| author_variant | a m m am amm h j h hj hjh |
| building | Verbundindex |
| bvnumber | BV044711962 |
| classification_rvk | SK 800 |
| collection | ZDB-23-DGG ZDB-94-OAB ZDB-23-GOA |
| ctrlnum | (ZDB-94-OAB)DOAB25429 (OCoLC)1001339463 (DE-599)DNB1137845163 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9783110562545 |
| format | Book |
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| id | DE-604.BV044711962 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T07:17:53Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110562538 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030108473 |
| oclc_num | 1001339463 |
| open_access_boolean | 1 |
| owner | DE-B1533 DE-M100 DE-12 DE-634 DE-210 DE-1052 DE-521 DE-1102 DE-1046 DE-1047 DE-1028 DE-Aug4 DE-1050 DE-573 DE-M347 DE-92 DE-1051 DE-898 DE-BY-UBR DE-859 DE-860 DE-1049 DE-861 DE-863 DE-BY-FWS DE-862 DE-BY-FWS DE-523 DE-Re13 DE-BY-UBR DE-Y3 DE-255 DE-Y7 DE-Y2 DE-70 DE-2174 DE-127 DE-22 DE-BY-UBG DE-155 DE-BY-UBR DE-150 DE-154 DE-83 DE-91 DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-20 DE-706 DE-824 DE-29 DE-29T DE-739 |
| owner_facet | DE-B1533 DE-M100 DE-12 DE-634 DE-210 DE-1052 DE-521 DE-1102 DE-1046 DE-1047 DE-1028 DE-Aug4 DE-1050 DE-573 DE-M347 DE-92 DE-1051 DE-898 DE-BY-UBR DE-859 DE-860 DE-1049 DE-861 DE-863 DE-BY-FWS DE-862 DE-BY-FWS DE-523 DE-Re13 DE-BY-UBR DE-Y3 DE-255 DE-Y7 DE-Y2 DE-70 DE-2174 DE-127 DE-22 DE-BY-UBG DE-155 DE-BY-UBR DE-150 DE-154 DE-83 DE-91 DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-20 DE-706 DE-824 DE-29 DE-29T DE-739 |
| physical | XXII, 582 Seiten Illustrationen |
| psigel | ZDB-23-DGG ZDB-94-OAB ZDB-23-GOA |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter textbook |
| spellingShingle | Mathai, Arakaparampil M. 1935- Haubold, Hans J. 1951- Probability and statistics a course for physicists and engineers Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4056995-0 |
| title | Probability and statistics a course for physicists and engineers |
| title_auth | Probability and statistics a course for physicists and engineers |
| title_exact_search | Probability and statistics a course for physicists and engineers |
| title_full | Probability and statistics a course for physicists and engineers Arak M. Mathai and Hans J. Haubold |
| title_fullStr | Probability and statistics a course for physicists and engineers Arak M. Mathai and Hans J. Haubold |
| title_full_unstemmed | Probability and statistics a course for physicists and engineers Arak M. Mathai and Hans J. Haubold |
| title_short | Probability and statistics |
| title_sort | probability and statistics a course for physicists and engineers |
| title_sub | a course for physicists and engineers |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung Statistik |
| url | https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=25429 https://doi.org/10.1515/9783110562545 https://www.degruyter.com/view/product/495845 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030108473&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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