Mathematical Methods of Statistics

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Princeton University Press, 1945 - Mathematics - 575 pages
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In this classic of statistical mathematical theory, Harald Cramér joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. The result of Cramér's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow.

For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance.

 

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Contents

II
3
III
10
IV
15
V
19
VI
33
VII
48
VIII
62
IX
76
XXIII
260
XXIV
291
XXV
301
XXVI
310
XXVII
317
XXVIII
321
XXIX
323
XXX
332

X
85
XI
89
XII
103
XIII
122
XIV
135
XV
137
XVI
151
XVII
166
XVIII
192
XIX
208
XX
233
XXI
244
XXII
255
XXXI
341
XXXII
363
XXXIII
378
XXXIV
416
XXXV
452
XXXVI
473
XXXVII
497
XXXVIII
507
XXXIX
525
XL
536
XLI
548
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About the author (1945)

Harald Cramér was Professor of Actuarial Mathematics and Mathematical Statistics, and director of the Institute of Mathematical Statistics at the University of Stockholm.

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