Statistical distributions:
Gespeichert in:
| Vorheriger Titel: | Evans, Merran Statistical distributions |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2011
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 212 S. graph. Darst. |
| ISBN: | 9780470390634 |
Internformat
MARC
| LEADER | 00000nam a22000002c 4500 | ||
|---|---|---|---|
| 001 | BV036501598 | ||
| 003 | DE-604 | ||
| 005 | 20220329 | ||
| 007 | t | ||
| 008 | 100614s2011 xxud||| |||| 00||| eng d | ||
| 010 | |a 2009052131 | ||
| 020 | |a 9780470390634 |9 978-0-470-39063-4 | ||
| 035 | |a (OCoLC)705587087 | ||
| 035 | |a (DE-599)BVBBV036501598 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c XD-US | ||
| 049 | |a DE-20 |a DE-945 |a DE-11 |a DE-M49 |a DE-521 |a DE-19 |a DE-29T |a DE-703 |a DE-824 | ||
| 050 | 0 | |a QA273.6 | |
| 082 | 0 | |a 519.2/4 | |
| 084 | |a QH 233 |0 (DE-625)141548: |2 rvk | ||
| 084 | |a SK 835 |0 (DE-625)143260: |2 rvk | ||
| 084 | |a MAT 603f |2 stub | ||
| 245 | 1 | 0 | |a Statistical distributions |c Catherine Forbes ... |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2011 | |
| 300 | |a XVIII, 212 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Forbes, Catherine Scipione |e Sonstige |0 (DE-588)171515390 |4 oth | |
| 780 | 0 | 0 | |i Bis 3. Aufl. u.d.T. |a Evans, Merran |t Statistical distributions |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020424004&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020424004 | ||
Datensatz im Suchindex
| _version_ | 1804143066196475904 |
|---|---|
| adam_text | Contents
Preface
xvii
1.
Introduction
1
2.
Terms and Symbols
3
2.1
Probability, Random Variable,
Variate,
and Number
3
Probabilistic Experiment
3
Sample Space
3
Random Variable
3
Variate
3
Random Number
4
2.2
Range, Quantile, Probability Statement, and Domain
4
Range
4
Quantile
5
Probability Statement
5
Probability Domain
5
2.3
Distribution Function and Survival Function
5
Distribution Function
5
Survival Function
6
2.4
Inverse Distribution Function and Inverse Survival Function
7
Inverse Survival Function
8
2.5
Probability Density Function and Probability Function
8
2.6
Other Associated Functions and Quantities
9
3.
General
Varíate
Relationships
15
3.1
Introduction
15
3.2
Function of
a Variate
15
3.3
One-to-One Transformations and Inverses
16
Inverse of a One-to-One Function
17
3.4
Variate
Relationships Under One-to-One Transformation
17
Probability Statements
17
Distribution Function
17
Inverse Distribution Function
18
Equivalence of
Variâtes
18
Inverse Function of
a Variate
18
vii
viii Contents
3.5 Parameters,
Variate,
and Function Notation
19
Variate
and Function Notation
19
3.6
Transformation of Location and Scale
20
3.7
Transformation from the Rectangular
Variate
20
3.8
Many-to-One Transformations
22
Symmetrical Distributions
22
4.
Multivariate Distributions
24
4.1
Joint Distributions
24
Joint Range
24
Bivariate Quantile
24
Joint Probability Statement
24
Joint Probability Domain
25
Joint Distribution Function
25
Joint Probability Density Function
25
Joint Probability Function
25
4.2
Marginal Distributions
26
Marginal Probability Density Function and Marginal
Probability Function
26
4.3
Independence
27
4.4
Conditional Distributions
28
Conditional Probability Function and Conditional
Probability Density Function
28
Composition
29
4.5
Bayes
Theorem
30
4.6
Functions of a Multivariate
30
5.
Stochastic Modeling
32
5.1
Introduction
32
5.2
Independent
Variâtes
32
5.3
Mixture Distributions
33
Finite Mixture
33
Infinite Mixture of Distributions
35
5.4
Skew-Symmetric Distributions
38
5.5
Distributions Characterized by Conditional Skewness
39
5.6
Dependent
Variâtes
42
6.
Parameter Inference
44
6.1
Introduction
44
6.2
Method of Percentiles Estimation
44
6.3
Method of Moments Estimation
45
6.4
Maximum Likelihood Inference
47
Properties of MLEs
47
Approximate Sampling Distribution for Fixed
η
48
Contents ix
6.5 Bayesian
Inference
50
Marginal Posteriors
51
7.
Bernoulli Distribution
53
7.1
Random Number Generation
53
7.2
Curtailed Bernoulli Trial Sequences
53
7.3
Urn Sampling Scheme
54
7.4
Note
54
8.
Beta Distribution
55
8.1
Notes on Beta and Gamma Functions
56
Definitions
56
Interrelationships
56
Special Values
57
Alternative Expressions
57
8.2
Variate
Relationships
57
8.3
Parameter Estimation
59
8.4
Random Number Generation
60
8.5
Inverted Beta Distribution
60
8.6
Noncentral
Beta Distribution
61
8.7
Beta Binomial Distribution
61
9.
Binomial Distribution
62
9.1
Variate
Relationships
64
9.2
Parameter Estimation
65
9.3
Random Number Generation
65
10.
Cauchy Distribution
66
10.1
Note
66
10.2
Variate
Relationships
67
10.3
Random Number Generation
68
10.4
Generalized Form
68
11.
Chi-Squared Distribution
69
11.1
Variate
Relationships
71
11.2
Random Number Generation
72
11.3
Chi Distribution
73
12.
Chi-Squared
(Noncentral)
Distribution
74
12.1
Variate
Relationships
75
χ
Contents
13. Dirichlet
Distribution
77
13.1
Variate
Relationships
77
13.2
Dirichlet
Multinomial Distribution
78
14.
Empirical Distribution Function
79
14.1
Estimation from Uncensored Data
79
14.2
Estimation from Censored Data
79
14.3
Parameter Estimation
81
14.4
Example
81
14.5
Graphical Method for the Modified Order-Numbers
81
14.6
Model Accuracy
83
15. Erlang
Distribution
84
15.1
Variate
Relationships
85
15.2
Parameter Estimation
85
15.3
Random Number Generation
85
16.
Error Distribution
86
16.1
Note
87
16.2
Variate
Relationships
87
17.
Exponential Distribution
88
17.1
Note
89
17.2
Variate
Relationships
91
17.3
Parameter Estimation
92
17.4
Random Number Generation
92
18.
Exponential Family
93
18.1
Members of the Exponential Family
93
18.2
Umvariate One-Parameter Exponential Family
93
18.3
Parameter Estimation
95
18.4
Generalized Exponential Distributions
95
Generalized Student s
t
Distribution
95
Variate
Relationships
96
Generalized Exponential Normal Distribution
96
Generalized
Lognormal
Distribution
96
Variate
Relationships
97
Contents xi
19. Extreme
Value
(Gumbel) Distribution 98
19.1 Note 99
19.2
Variate
Relationships
100
19.3 Parameter
Estimation
101
19.4
Random Number
Generation 101
20.
F
(Variance
Ratio) or Fisher-Snedecor Distribution
102
20.1
Variate
Relationships
103
21.
ŕ1
(Noncentral)
Distribution
107
21.1
Variate
Relationships
108
22.
Gamma Distribution
109
22.1
Variate
Relationships
110
22.2
Parameter Estimation
111
22.3
Random Number Generation
112
22.4
Inverted Gamma Distribution
112
22.5
Normal Gamma Distribution
112
22.6
Generalized Gamma Distribution
113
Variate
Relationships
113
23.
Geometric Distribution
114
23.1
Notes
115
23.2
Variate
Relationships
115
23.3
Random Number Generation
116
24.
Hypergeometnc
Distribution
117
24.1
Note
118
24.2
Variate
Relationships
118
24.3
Parameter Estimation
1)8
24.4
Random Number Generation
119
24.5
Negative Hypergeometric Distribution
119
24.6
Generalized Hypergeometric Distribution
119
25.
Inverse Gaussian
(Wald)
Distribution
120
25.1
Variate
Relationships
121
25.2
Parameter Estimation
121
xii Contents
26.
Laplace
Distribution 122
26.1
Variate
Relationships
124
26.2
Parameter Estimation
124
26.3
Random Number Generation
124
27.
Logarithmic Series Distribution
125
27.1
Variate
Relationships
126
27.2
Parameter Estimation
126
28.
Logistic Distribution
127
28.1
Notes
128
28.2
Variate
Relationships
128
28.3
Parameter Estimation
130
28.4
Random Number Generation
130
29. Lognormal
Distribution
131
29.1
Variate
Relationships
132
29.2
Parameter Estimation
134
29.3
Random Number Generation
134
30.
Multinomial Distribution
135
30.1
Variate
Relationships
136
30.2
Parameter Estimation
136
31.
Multivariate Normal
(Multinormal)
Distribution
137
31.1
Variate
Relationships
138
31.2
Parameter Estimation
138
32.
Negative Binomial Distribution
139
32.1
Note
140
32.2
Variate
Relationships
141
32.3
Parameter Estimation
142
32.4
Random Number Generation
142
33.
Normal (Gaussian) Distribution
143
33.1
Variate
Relationships
144
33.2
Parameter Estimation
147
Contents xiii
33.3
Random Number Generation
147
33.4
Truncated Normal Distribution
147
33.5
Variate
Relationships
148
34.
Pareto Distribution
149
34.1
Note
149
34.2
Variate
Relationships
150
34.3
Parameter Estimation
151
34.4
Random Number Generation
151
35.
Poisson
Distribution
152
35.1
Note
153
35.2
Variate
Relationships
153
35.3
Parameter Estimation
156
35.4
Random Number Generation
156
36.
Power Function Distribution
157
36.1
Variate
Relationships
157
36.2
Parameter Estimation
159
36.3
Random Number Generation
159
37.
Power Series (Discrete) Distribution
160
37.1
Note
160
37.2
Variate
Relationships
161
37.3
Parameter Estimation
161
38.
Queuing Formulas
162
38.1
Characteristics of Queuing Systems and Kendall-Lee Notation
162
Characteristics of Queuing Systems
162
Kendall-Lee Notation
164
38.2
Definitions, Notation, and Terminology
164
Steady State
164
Traffic Intensity and Traffic Density
164
Notation and Terminology
164
38.3
General Formulas
166
38.4
Some Standard Queuing Systems
166
The M/M/VG/oo/oo System
166
The M/M/s/G/ oo/oo System
166
The M/G/l/G/oo/ oo System (Pollaczek-Khinchin)
168
The M/MA/G/m/oo System
168
The M/G/m/G/m/oo System
(Erlang) 169
xiv Contents
The
M/Mñ/G/N/N System
(One Server, Finite Population N)
169
The M/M/s/G/N/N System
(s
Servers, Finite Population N)
171
39.
Rayleigh Distribution
173
39.1
Variate
Relationships
173
39.2
Parameter Estimation
175
40.
Rectangular (Uniform) Continuous Distribution
176
40.1
Variate
Relationships
177
40.2
Parameter Estimation
179
40.3
Random Number Generation
179
41.
Rectangular (Uniform) Discrete Distribution
180
41.1
General Form
181
41.2
Parameter Estimation
182
42.
Student s
í
Distribution
183
42.1
Variate
Relationships
185
42.2
Random Number Generation
186
43.
Student s
í
(Noncentral)
Distribution
187
43.1
Variate
Relationships
188
44.
Triangular Distribution
189
44.1
Variate
Relationships
189
44.2
Random Number Generation
190
45. von
Mises
Distribution
191
45.1
Note
191
45.2
Variate
Relationships
192
45.3
Parameter Estimation
192
46.
Weibull Distribution
193
46.1
Note
195
46.2
Variate
Relationships
196
46.3
Parameter Estimation
196
46.4
Random Number Generation
196
Contents xv
46.5
Three-Parameter
Weibull Distribution 196
46.6
Three-Parameter Weibull Random Number
Generation 198
46.7 Bi-Weibull Distribution 198
46.8
Five-Parameter
Bi-
Weibull Distribution 198
Bi-Weibull
Random Number
Generation 200
Bi-Weibull
Graphs
200
46.9
WeibuU
Family 201
47.
Wishart
(Central) Distribution 202
47.1 Note 203
47.2
Variate
Relationships
203
48.
Statistical Tables
204
Table
48.1:
Normal Distribution Function
-FnÍx)
205
Table
48.2:
Percentiles of the Chi-Squared
χ2
:
ν
Distribution, G(l
-
a)
206
Table
48.3:
Percentiles of the
F
:
ν, ω
Distribution
207
Table
48.4:
Percentiles of the Student s
/
Distribution
209
Table
48.5:
Partial Expectations for the Standard Normal Distribution
210
Bibliography
211
|
| any_adam_object | 1 |
| author_GND | (DE-588)171515390 |
| building | Verbundindex |
| bvnumber | BV036501598 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.6 |
| callnumber-search | QA273.6 |
| callnumber-sort | QA 3273.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 SK 835 |
| classification_tum | MAT 603f |
| ctrlnum | (OCoLC)705587087 (DE-599)BVBBV036501598 |
| 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 |
| edition | 4. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01658nam a22004332c 4500</leader><controlfield tag="001">BV036501598</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220329 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100614s2011 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2009052131</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780470390634</subfield><subfield code="9">978-0-470-39063-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)705587087</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036501598</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-945</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-M49</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA273.6</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2/4</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 233</subfield><subfield code="0">(DE-625)141548:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 835</subfield><subfield code="0">(DE-625)143260:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 603f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Statistical distributions</subfield><subfield code="c">Catherine Forbes ...</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">4. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, NJ</subfield><subfield code="b">Wiley</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 212 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="C">b</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Forbes, Catherine Scipione</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)171515390</subfield><subfield code="4">oth</subfield></datafield><datafield tag="780" ind1="0" ind2="0"><subfield code="i">Bis 3. Aufl. u.d.T.</subfield><subfield code="a">Evans, Merran</subfield><subfield code="t">Statistical distributions</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020424004&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020424004</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV036501598 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:41:45Z |
| institution | BVB |
| isbn | 9780470390634 |
| language | English |
| lccn | 2009052131 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020424004 |
| oclc_num | 705587087 |
| open_access_boolean | |
| owner | DE-20 DE-945 DE-11 DE-M49 DE-BY-TUM DE-521 DE-19 DE-BY-UBM DE-29T DE-703 DE-824 |
| owner_facet | DE-20 DE-945 DE-11 DE-M49 DE-BY-TUM DE-521 DE-19 DE-BY-UBM DE-29T DE-703 DE-824 |
| physical | XVIII, 212 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| spelling | Statistical distributions Catherine Forbes ... 4. ed. Hoboken, NJ Wiley 2011 XVIII, 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Distribution (Probability theory) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s b DE-604 Forbes, Catherine Scipione Sonstige (DE-588)171515390 oth Bis 3. Aufl. u.d.T. Evans, Merran Statistical distributions Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020424004&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Statistical distributions Distribution (Probability theory) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4151278-9 |
| title | Statistical distributions |
| title_auth | Statistical distributions |
| title_exact_search | Statistical distributions |
| title_full | Statistical distributions Catherine Forbes ... |
| title_fullStr | Statistical distributions Catherine Forbes ... |
| title_full_unstemmed | Statistical distributions Catherine Forbes ... |
| title_old | Evans, Merran Statistical distributions |
| title_short | Statistical distributions |
| title_sort | statistical distributions |
| topic | Distribution (Probability theory) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Distribution (Probability theory) Wahrscheinlichkeitsverteilung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020424004&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT forbescatherinescipione statisticaldistributions |