Statistical and computational methods in data analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland
1976
|
| Ausgabe: | 2., rev. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 414 S. graph. Darst. |
| ISBN: | 0444108939 |
Internformat
MARC
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| 240 | 1 | 0 | |a Statistische Methoden der Datenanalyse |
| 245 | 1 | 0 | |a Statistical and computational methods in data analysis |c Siegmund Brandt |
| 250 | |a 2., rev. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1976 | |
| 300 | |a XVIII, 414 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Mathematical statistics | |
| 650 | 4 | |a Probabilities | |
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Datensatz im Suchindex
| _version_ | 1804117292000215040 |
|---|---|
| adam_text | Titel: Statistical and computational methods in data analysis
Autor: Brandt, Siegmund
Jahr: 1976
CONTENTS
Preface
............................
v
Contents..................
vu
List
of
examples
........................
xi
List
of
FORTRAN
programs..................
xv
List
of
frequently
used
symbols.................
xvn
1.
introduction.........................
1
2.
Probabilities.........................
4
2-1.
Experiments,
events,
sample
space............
4
2-2.
The
concept
of
probability...............
5
2-
3.
Rules
of
probability
calculus;
conditional
probability
...
7
Exercises.......................
9
3.
Random
variables;
distributions
of
a
random
variable.......
10
3-
1.
Random
variables...................
10
3-2.
Distributions
of
one
random
variable...........
10
3-3.
Functions
of
one
random
variable,
expectation
value,
variance,
moments.......................
12
3-
4.
Chebychev’s
inequality.................
18
Exercises.......................
19
4.
Distributions
of
several
random
variables............
20
4-
1.
Distribution
function
and
probability
density
of
two
variables;
conditional
probability.................
20
4-2.
Expectation
values,
variances,
covariances
and
correlation
coefficient.......................
22
4-3.
More
than
two
variables;
vector
and
matrix
notation.
...
25
4-4.
Transformation
of
variables...............
28
4-
5.
Linear
and
orthogonal
transformations;
propagation
of
errors
32
Exercises.......................
37
5.
Some
important
distributions
and
theorems...........
39
5-
1.
Binomial
and
multinomial
distributions.........
39
vru
CONTENTS
5-2.
Frequency;
the
law
of
large
numbers..........
42
5-3.
Hypergeometric
distribution..............
43
5-4.
Poisson
distribution..................
47
5-5.
Uniform
distribution
and
an
application:
the
Monte
Carlo
method.......................
52
5-5.1.
Probability
density,
expectation
value,
variance
...
52
5-5.2.
Generation
of
uniformly
distributed
random
numbers
by
computers
.................
53
5-5.3.
Generation
of
any
distribution
by
transformation
of
the
uniform
distribution.............
54
5-6.
The
characteristic
function
of
a
distribution.......
62
5-7.
The
Laplace
model
of
errors..............
64
5-8.
Normal
distribution..................
67
5-9.
Quantitative
properties
of
the
normal
distribution.....
69
5-10.
Multivariate
normal
distribution............
72
5-11.
The
central
limit
theorem...............
78
5-12.
Experimental
errors
and
normal
distribution;
Herschel’s
model........................
79
5-
13.
Convolution
of
distributions..............
82
5-13.1.
Folding
integrals................
82
5-13.2.
Convolution
with
the
normal
distribution.....
85
Exercises.......................
89
6.
Sampling..........................
92
6-
1.
Random
sampling;
distribution
of
a
sample;
estimates
...
92
6-2.
Sampling
from
continuous
populations..........
95
6-3.
Sampling
from
partitioned
distributions..........
97
6-4.
Sampling
without
replacement
from
finite
populations;
mean
square
deviation;
degrees
of
freedom...........
102
6-5.
Sampling
from
normal
distributions;
^-distribution
....
107
6-6.
X
2
and
empirical
variance................
Ill
6-7.
Sampling
by
counting.
Small
samples...........
113
6-
8.
Numerical
and
graphical
analysis
of
sampled
data
with
com¬
puter
programs....................
118
6-8.1.
Scatter
diagram
and
histogram
of
a
one-dimensional
sample.....................
118
6-8.2.
Scatter
diagram
of
a
two-dimensional
sample
....
125
Exercises.......................
131
7.
The
method
of
“maximum
likelihood”..............
133
7-
1.
Likelihood
quotient;
likelihood
function.........
133
7-2.
The
concept
of
maximum
likelihood...........
135
7-3.
Information
inequality;
minimum
variance
and
sufficient
estimates.......................
138
7-4.
Asymptotic
properties
of
the
likelihood
function
and
of
maxi¬
mum
likelihood
estimators...............
145
CONTENTS
IX
7-5.
Solution
of
the
likelihood
equation
by
iteration......
147
7-6.
Simultaneous
estimation
of
several
parameters.......
148
7-7.
Uniqueness
of
the
method;
confidence
interval.......
152
7-
8.
Bartlett’s
5-function..................
154
Exercises.......................
157
8.
Testing
of
statistical
hypotheses................
158
8-
1.
F-test
on
equality
of
variances..............
160
8-2.
Student’s
test;
comparison
of
means...........
164
8-3.
Some
aspects
of
a
general
theory
of
tests.........
169
8-4.
Neyman-Pearson
theorem
and
applications........
174
8-5.
The
likelihood
ratio
method...............
177
8-
6.
The
x
2
-test
on
goodness
of
fit..............
182
Exercises.......................
189
9.
The
method
of
least
squares..................
191
9-
1.
Direct
measurements
with
equal
or
different
accuracy.
.
.
.
191
9-2.
Indirect
measurements.................
196
9-2.1.
The
linear
case..................
196
9-2.2.
The
non-linear
case................
204
9-2.3.
Properties
of
the
least
squares
solution;
x
2
-test.
...
210
9-3.
Constrained
measurements...............
213
9-3.1.
The
method
of
elements..............
214
9-3.2.
The
method
of
Lagrangian
multipliers.......
216
9-4.
The
general
case
of
least
squares
fitting..........
221
9-
5.
A
FORTRAN
program
for
general
least
squares
fitting;
examples.......................
224
Exercises.......................
239
10.
Some
remarks
on
minimization................
242
10-
1.
Parameter
estimation
and
minimization.........
242
10-
2.
Different
minimization
procedures............
243
11.
Analysis
of
variance.....................
250
11-
1.
One-way
classification.................
250
11-2.
Some
aspects
of
two-way
classification..........
255
11-
3.
A
FORTRAN
program
for
two-way
classification.....
264
Exercises.......................
269
12.
Linear
regression......................
270
12-
1.
Linear
regression
as
a
simple
case
of
least
squares.....
270
12-2.
Confidence
intervals..................
274
12-3.
Testing
of
hypotheses
.................
275
12-4.
Linear
regression
and
analysis
of
variance........
276
x
CONTENTS
12-5.
A
general
FORTRAN
program
for
linear
regression.
.
.
.
277
12-
6.
Interpretation
of
results
from
linear
regression......
284
Exercises.......................
289
13.
Time
series
analysis..................
291
13-
1.
Time
series.
Trend..................
291
13-2.
Moving
averages...................
292
13-3.
End
effects......................
296
13-4.
Confidence
interval..................
296
13-5.
A
FORTRAN
program
for
time
series
analysis......
298
13-6.
A
word
of
caution..................
301
Exercise.......................
305
Solution
and
discussion
of
the
exercises..............
306
APPENDICES
A.
Some
elements
of
the
FORTRAN
programming
language.....
329
B.
Short
review
of
matrix
calculus................
340
B-l.
Definitions
of
matrices
and
vectors............
340
B-2.
Equality,
addition,
subtraction
and
multiplication
of
matrices
343
B-3.
Determinant
and
inverse
of
a
square
matrix;
solution
of
matrix
equations.......................
347
B-4.
FORTRAN
programs
for
matrix
handling........
354
C.
Elements
of
combinatorial
analysis..............
364
D.
Euler’s
gamma-function...................
367
E.
Collection
of
important
formulae...............
369
F.
Statistical
tables......................
389
F-l.
Poisson
distribution..................
389
F-2.
Normal
distribution
function..............
392
F-3.
Fractiles
of
the
normal
distribution...........
395
F-4.
^-distribution
function.................
398
F-5.
Fractiles
of
/^distribution...............
400
F-6.
F-iest........................
401
F-7.
Fractiles
for
Student’s
test...............
406
F-8.
Random
numbers...................
407
References
and
bibliography...................
408
Subject
index.........................
411
Index
to
FORTRAN
statements
and
FORTRAN
programs
used
in
this
book.......•....................
415
|
| any_adam_object | 1 |
| author | Brandt, Siegmund 1936-2016 |
| author_GND | (DE-588)137314329 |
| author_facet | Brandt, Siegmund 1936-2016 |
| author_role | aut |
| author_sort | Brandt, Siegmund 1936-2016 |
| author_variant | s b sb |
| building | Verbundindex |
| bvnumber | BV003002933 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276 |
| callnumber-search | QA276 |
| callnumber-sort | QA 3276 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 231 |
| ctrlnum | (OCoLC)253969638 (DE-599)BVBBV003002933 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2., rev. ed. |
| format | Book |
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| id | DE-604.BV003002933 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:52:05Z |
| institution | BVB |
| isbn | 0444108939 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001879921 |
| oclc_num | 253969638 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XVIII, 414 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | North-Holland |
| record_format | marc |
| spelling | Brandt, Siegmund 1936-2016 Verfasser (DE-588)137314329 aut Statistische Methoden der Datenanalyse Statistical and computational methods in data analysis Siegmund Brandt 2., rev. ed. Amsterdam [u.a.] North-Holland 1976 XVIII, 414 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Datenauswertung (DE-588)4131193-0 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Statistik (DE-588)4056995-0 s 1\p DE-604 Statistische Analyse (DE-588)4116599-8 s 2\p DE-604 Datenauswertung (DE-588)4131193-0 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001879921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brandt, Siegmund 1936-2016 Statistical and computational methods in data analysis Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Statistische Analyse (DE-588)4116599-8 gnd Datenanalyse (DE-588)4123037-1 gnd Datenauswertung (DE-588)4131193-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4116599-8 (DE-588)4123037-1 (DE-588)4131193-0 |
| title | Statistical and computational methods in data analysis |
| title_alt | Statistische Methoden der Datenanalyse |
| title_auth | Statistical and computational methods in data analysis |
| title_exact_search | Statistical and computational methods in data analysis |
| title_full | Statistical and computational methods in data analysis Siegmund Brandt |
| title_fullStr | Statistical and computational methods in data analysis Siegmund Brandt |
| title_full_unstemmed | Statistical and computational methods in data analysis Siegmund Brandt |
| title_short | Statistical and computational methods in data analysis |
| title_sort | statistical and computational methods in data analysis |
| topic | Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Statistische Analyse (DE-588)4116599-8 gnd Datenanalyse (DE-588)4123037-1 gnd Datenauswertung (DE-588)4131193-0 gnd |
| topic_facet | Mathematical statistics Probabilities Statistik Statistische Analyse Datenanalyse Datenauswertung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001879921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brandtsiegmund statistischemethodenderdatenanalyse AT brandtsiegmund statisticalandcomputationalmethodsindataanalysis |