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Acts of God and ManRuminations on Risk and Insurance$
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Michael Powers

Print publication date: 2014

Print ISBN-13: 9780231153676

Published to Columbia Scholarship Online: November 2015

DOI: 10.7312/columbia/9780231153676.001.0001

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The Value of Experience

The Value of Experience

Independence and Estimation

Chapter:
(p.53) 4 The Value of Experience
Source:
Acts of God and Man
Author(s):

Michael R. Powers

Publisher:
Columbia University Press
DOI:10.7312/columbia/9780231153676.003.0004

This chapter explores a number of concepts and methods employed in the frequency/classical approach, called frequentism. To present the standard frequentist paradigm, it begins by defining the concept of a random sample, and then summarizes how such samples are used to construct both point and interval estimates. Next, it introduces three important asymptotic results—the law of large numbers, the central limit theorem, and the generalized central limit theorem—followed by a discussion of the practical validity of the independence assumption underlying random samples. Finally, it considers in some detail the method of hypothesis testing, whose framework follows much the same logic as both the U.S. criminal justice system and the scientific method as it is generally understood.

Keywords:   probability interpretations, probability estimation, frequentism, random sample, hypothesis testing, frequentist paradigm

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