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Books > Science & Mathematics > Mathematics > Probability & statistics
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Probability With a View Towards Statistics, Two Volume Set (Hardcover)
Loot Price: R5,386
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Probability With a View Towards Statistics, Two Volume Set (Hardcover)
Series: Chapman & Hall/CRC Probability Series
Expected to ship within 12 - 17 working days
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Volume I of this two-volume text and reference work begins by
providing a foundation in measure and integration theory. It then
offers a systematic introduction to probability theory, and in
particular, those parts that are used in statistics. This volume
discusses the law of large numbers for independent and
non-independent random variables, transforms, special
distributions, convergence in law, the central limit theorem for
normal and infinitely divisible laws, conditional expectations and
martingales. Unusual topics include the uniqueness and convergence
theorem for general transforms with characteristic functions,
Laplace transforms, moment transforms and generating functions as
special examples. The text contains substantive applications, e.g.,
epidemic models, the ballot problem, stock market models and water
reservoir models, and discussion of the historical background. The
exercise sets contain a variety of problems ranging from simple
exercises to extensions of the theory. Volume II of this two-volume
text and reference work concentrates on the applications of
probability theory to statistics, e.g., the art of calculating
densities of complicated transformations of random vectors,
exponential models, consistency of maximum estimators, and
asymptotic normality of maximum estimators. It also discusses
topics of a pure probabilistic nature, such as stochastic
processes, regular conditional probabilities, strong Markov chains,
random walks, and optimal stopping strategies in random games.
Unusual topics include the transformation theory of densities using
Hausdorff measures, the consistency theory using the upper
definition function, and the asymptotic normality of maximum
estimators using twice stochastic differentiability. With an
emphasis on applications to statistics, this is a continuation of
the first volume, though it may be used independently of that book.
Assuming a knowledge of linear algebra and analysis, as well as a
course in modern probability, Volume II looks at statistics from a
probabilistic point of view, touching only slightly on the
practical computation aspects.
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