Dieses Buch ist eine leicht verständliche Einführung in die Statistik, die typische Schlussweisen der Mathematischen Statistik exemplarisch erläutert: Warum kann aus den Ergebnissen einer Stichprobenunt...
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ISBN:
(数字)9783662637128
ISBN:
(纸本)9783662637111
Dieses Buch ist eine leicht verständliche Einführung in die Statistik, die typische Schlussweisen der Mathematischen Statistik exemplarisch erläutert: Warum kann aus den Ergebnissen einer Stichprobenuntersuchung auf die Gesamtheit geschlossen werden? Welche Ungenauigkeiten und Unsicherheiten sind dabei möglich? Wie und warum können zufallsbedingte Abweichungen mit mathematischen Methoden analysiert werden?;Für die 2. Auflage wurde das Buch aktualisiert und um Musterlösungen bzw. Lösungshinweise zu den meisten Aufgaben sowie um eine Einführung in das kostenlose Programm;ergänzt, mit dem sich viele Berechnungen stark vereinfachen lassen.
The book of nature, according to Galilei, is written in the language of mat- matics. The nature of mathematics is being exact, and its exactness is und- lined by the formalism used by mathematicians to write it. This ...
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ISBN:
(数字)9780387733944
ISBN:
(纸本)9780387733937
The book of nature, according to Galilei, is written in the language of mat- matics. The nature of mathematics is being exact, and its exactness is und- lined by the formalism used by mathematicians to write it. This formalism, characterized by theorems and proofs, and syncopated with occasional l- mas, remarks and corollaries, is so deeply ingrained that mathematicians feel uncomfortable when the pattern is broken, to the point of giving the - pression that the attitude of mathematicians towards the way mathematics should be written is almost moralistic. There is a de?nition often quoted, “A mathematician is a person who proves theorems”, and a similar, more alchemistic one, credited to Paul Erd? os, but more likely going back to Alfr´ ed R´ enyi,statingthat“Amathematicianisamachinethattransformsco?eeinto 1 theorems ”. Therefore it seems to be the form, not the content, that char- terizes mathematics, similarly to what happens in any formal moralistic code wherein form takes precedence over content. This book is deliberately written in a very di?erent manner, without a single theorem or proof. Since morality has its subjective component, to pa- phrase Manuel Vasquez Montalban, we could call it Ten Immoral Mathemat- 2 ical Recipes . Does the lack of theorems and proofs mean that the book is more inaccurate than traditional books of mathematics? Or is it possibly just a sign of lack of co?ee? This is our ?rst open question. Exactness is an interesting concept.
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently ...
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ISBN:
(数字)9789401735155
ISBN:
(纸本)9780792326083;9789048143467
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
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