A normal distribution course:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Frankfurt am Main [u.a.]
Lang
2004
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 221 S. Ill., graph. Darst. 21 cm |
| ISBN: | 3631529341 0820473480 |
Internformat
MARC
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| 100 | 1 | |a Groß, Jürgen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A normal distribution course |c Jürgen Groß |
| 264 | 1 | |a Frankfurt am Main [u.a.] |b Lang |c 2004 | |
| 300 | |a XII, 221 S. |b Ill., graph. Darst. |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Normale verdeling |2 gtt | |
| 650 | 4 | |a Gaussian distribution | |
| 650 | 0 | 7 | |a Normalverteilung |0 (DE-588)4075494-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804133266753585152 |
|---|---|
| adam_text | JIIRGENGROG A NORMAL DISTRIBUTION COURSE PETER LANG FRANKFURT AM MAIN *
BERLIN * BERN * BRUXELLES * NEW YORK * OXFORD * WIEN CONTENTS DATA
ANALYSIS 1 1.1 DESCRIBING DATA 1 1.1.1 STATISTICAL SOFTWARE PACKAGES 2
1.1.2 OBSERVATIONS 2 1.1.3 FREQUENCY DISTRIBUTION 5 1.2 INFERENCE BASE 8
1.2.1 RANDOM VARIABLE 8 1.2.2 DISTRIBUTION OF A RANDOM VARIABLE 10 1.2.3
RANDOM SAMPLE 22 1.3 INFERENCE 23 1.3.1 ESTIMATION 24 1.3.2 SAMPLE MEAN
AND VARIANCE 31 1.3.3 MAXIMUM LIKELIHOOD ESTIMATION 34 1.3.4 FITTING
PROBABILITY DENSITY FUNCTIONS 38 1.4 A SUMMARY ILLUSTRATION 43 THE
NORMAL DISTRIBUTION 45 2.1 DEFINITION OF THE NORMAL DISTRIBUTION 46
2.1.1 LOCATION AND SCALE PARAMETER 46 2.1.2 EXPECTATION AND VARIANCE 48
2.1.3 ALTERNATIVE PARAMETRIZATIONS 49 2.2 STANDARD NORMAL DISTRIBUTION
50 2.2.1 THE FUNCTION 50 2.2.2 THE FUNCTION $(Z) 51 2.2.3 RELATED
FUNCTIONS 54 X CONTENTS 2.3 MOMENTS 56 2.3.1 THE 1, 2, 3 STANDARD
DEVIATION INTERVALS 56 2.3.2 HIGHER MOMENTS 57 2.3.3 SKEWNESS AND
KURTOSIS 58 2.3.4 SAMPLE SKEWNESS AND KURTOSIS 60 2.4 QUANTILES 61 2.4.1
QUANTILES OF THE NORMAL DISTRIBUTION . . 62 2.4.2 SAMPLE QUANTILES 65
2.5 PARAMETER ESTIMATION 67 2.5.1 MAXIMUM LIKELIHOOD ESTIMATORS 67 2.5.2
PROPERTIES OF ESTIMATORS 68 2.6 THE CENTRAL LIMIT THEOREM 71 2.6.1
APPROXIMATE NORMALITY OF THE SAMPLE MEAN . . . . 71 2.6.2 CAUTIONARY
NOTES 75 2.6.3 APPROXIMATE NORMALITY OF SAMPLE STATISTICS 76 2.7
APPROXIMATE NORMALITY OF THE BINOMIAL DISTRIBUTION .... 79 2.7.1 THE
BINOMIAL DISTRIBUTION 79 2.7.2 APPROXIMATION BY THE NORMAL DISTRIBUTION
81 2.7.3 THE GALTON BOARD 84 2.8 RANDOM SAMPLE GENERATION 85 3 CHECKING
FOR NORMALITY 89 3.1 SAMPLE CHARACTERISTIC VALUES 89 3.2 GRAPHICS 92
3.2.1 THE HISTOGRAM 92 3.2.2 THEECDF 95 3.2.3 THE NORMAL
QUANTILE-QUANTILE PLOT 97 3.3 SUMMARY 101 4 TESTING FOR NORMALITY 103
4.1 GENERAL REMARKS 103 4.1.1 SIGNIFICANCE TESTS 103 4.1.2
CLASSIFICATION OF TESTS 106 4.2 THE CHI-SQUARE TEST 107 4.3 TESTS BASED
ON THE ECDF 110 4.3.1 THE LILLIEFORS (KOLMOGOROV-SMIRNOV) TEST ILL 4.3.2
THE CRAMER-VON MISES TEST 114 CONTENTS XI 4.3.3 THE ANDERSON-DARLING
TEST 115 4.4 CORRELATION AND REGRESSION TESTS 116 4.4.1 THE
SHAPIRO-FRANCIA TEST 117 4.4.2 THE SHAPIRO-WILK TEST 118 4.5 SUMMARY 119
5 VARIANTS OF THE NORMAL DISTRIBUTION 121 5.1 TRUNCATED NORMAL
DISTRIBUTION 121 5.1.1 TRUNCATION OF THE NORMAL DISTRIBUTION 122 5.1.2
ESTIMATION OF PARAMETERS 125 5.1.3 RANDOM SAMPLE GENERATION 128 5.2
TWO-NORMALS-MIXTURE DISTRIBUTION 129 5.2.1 PROBABILITY DENSITY FUNCTION
130 5.2.2 ESTIMATION OF PARAMETERS 132 5.2.3 RANDOM SAMPLE GENERATION
139 5.3 SKEW-NORMAL DISTRIBUTION 139 5.3.1 PROBABILITY DENSITY FUNCTION
140 5.3.2 ESTIMATION OF PARAMETERS 143 5.3.3 RANDOM SAMPLE GENERATION
145 6 TRANSFORMATIONS TO NORMALITY 147 6.1 DATA TRANSFORMATION 147 6.2
THE JOHNSON SYSTEM OF DISTRIBUTIONS 148 6.2.1 THREE TYPES OF
DISTRIBUTION 148 6.2.2 ESTIMATION OF PARAMETERS 152 6.2.3 CHOICE OF FIT
158 6.3 THE LOGNORMAL DISTRIBUTION 158 6.3.1 TWO- AND THREE-PARAMETER
LOGNORMAL DISTRIBUTION 160 6.3.2 ESTIMATION OF PARAMETERS 161 6.4 POWER
TRANSFORMATIONS 163 6.4.1 BOX-COX TRANSFORMATION 163 6.4.2
TRANSFORMATION FOR PROPORTIONS 165 7 TWO NORMAL VARIABLES 169 7.1 THE
BIVARIATE NORMAL DISTRIBUTION 169 7.1.1 PROBABILITY DENSITY FUNCTION 170
7.1.2 SOME PROPERTIES 170 XII CONTENTS 7.1.3 UNCORRELATEDNESS AND
INDEPENDENCE 173 7.1.4 ESTIMATION 174 7.1.5 ASSESSING BIVARIATE
NORMALITY 174 7.1.6 RANDOM SAMPLE GENERATION 176 7.2 TWO NORMAL
VARIABLES 177 7.2.1 ARE TWO NORMALS JOINTLY NORMAL? 177 7.2.2 ARE TWO
UNCORRELATED NORMALS INDEPENDENT? .... 180 7.2.3 DOES UNCORRELATEDNESS
OF TWO NORMALS IMPLY INDE- PENDENCE ONLY IF THEY ARE JOINTLY NORMAL? 182
7.2.4 IS ANY LINEAR COMBINATION OF TWO NORMALS AGAIN NORMAL? 182 7.3
VECTOR AND MATRIX REPRESENTATION 183 8 TRANSFORMATIONS OF NORMAL
VARIABLES 185 8.1 FUNCTIONS OF A RANDOM VARIABLE 185 8.2 FUNCTIONS OF A
SINGLE NORMAL VARIABLE 187 8.2.1 DISTRIBUTION OF THE ABSOLUTE VALUE 187
8.2.2 DISTRIBUTION OF THE SQUARE 189 8.2.3 DISTRIBUTION OF THE
RECIPROCAL 191 8.2.4 DISTRIBUTION OF MINIMUM AND MAXIMUM 192 8.3
FUNCTIONS OF TWO INDEPENDENT NORMALS 193 8.3.1 DISTRIBUTION OF THE SUM
194 8.3.2 DISTRIBUTION OF PRODUCT AND QUOTIENT 194 8.4 FUNCTIONS RELATED
TO A NORMAL SAMPLE 197 8.4.1 STANDARD NORMAL SAMPLE 197 8.4.2
DISTRIBUTION OF PARAMETER-SAMPLE STATISTIC FUNCTIONS 204 8.4.3
DISTRIBUTION OF THE SAMPLE Z-SCORE 208 BIBLIOGRAPHY 211 INDEX 217
|
| any_adam_object | 1 |
| author | Groß, Jürgen |
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| dewey-full | 519.2/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/4 |
| dewey-search | 519.2/4 |
| dewey-sort | 3519.2 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:05:59Z |
| institution | BVB |
| isbn | 3631529341 0820473480 |
| language | English |
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| physical | XII, 221 S. Ill., graph. Darst. 21 cm |
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| publisher | Lang |
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| spelling | Groß, Jürgen Verfasser aut A normal distribution course Jürgen Groß Frankfurt am Main [u.a.] Lang 2004 XII, 221 S. Ill., graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Normale verdeling gtt Gaussian distribution Normalverteilung (DE-588)4075494-7 gnd rswk-swf Normalverteilung (DE-588)4075494-7 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013108204&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Groß, Jürgen A normal distribution course Normale verdeling gtt Gaussian distribution Normalverteilung (DE-588)4075494-7 gnd |
| subject_GND | (DE-588)4075494-7 |
| title | A normal distribution course |
| title_auth | A normal distribution course |
| title_exact_search | A normal distribution course |
| title_full | A normal distribution course Jürgen Groß |
| title_fullStr | A normal distribution course Jürgen Groß |
| title_full_unstemmed | A normal distribution course Jürgen Groß |
| title_short | A normal distribution course |
| title_sort | a normal distribution course |
| topic | Normale verdeling gtt Gaussian distribution Normalverteilung (DE-588)4075494-7 gnd |
| topic_facet | Normale verdeling Gaussian distribution Normalverteilung |
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