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Books on the topic 'Product of independent random variables'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces. Cambridge: Cambridge University Press, 1994.

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2

Arak, T. V. Uniform limit theorems for sums of independent random variables. Providence, R.I: American Mathematical Society, 1988.

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3

Petrov, V. V. Limit theorems of probability theory: Sequences of independent random variables. Oxford: Clarendon Press, 1995.

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4

Meerschaert, Mark M. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. New York, USA: John Wiley & Sons, 2001.

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5

Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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6

Lemeshko, Boris, and Irina Veretel'nikova. Criteria for testing hypotheses about randomness and the absence of a trend. Application Guide. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1587437.

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The monograph discusses the application of statistical criteria aimed at testing hypotheses about the absence of a trend in the analyzed samples. The rejection of such a hypothesis gives grounds to consider the analyzed data as samples of independent equally distributed random variables. We consider a set of special criteria aimed at testing such hypotheses, as well as a set of criteria for the uniformity of laws, the uniformity of averages and the uniformity of variances, which can also be used for these purposes. The disadvantages and advantages of various criteria are emphasized, the application of criteria in conditions of violation of standard assumptions is considered. Estimates of the power of the criteria are given, which allows you to navigate when choosing the most preferred criteria. Following the recommendations will ensure the correctness and increase the validity of statistical conclusions when analyzing data. It is intended for specialists who are interested in the application of statistical methods for the analysis of various aspects and trends of the surrounding reality and who are in contact with the processing of experimental results, the need for data analysis in their activities. It will be useful for engineers, researchers, specialists of various profiles (doctors, biologists, sociologists, economists, etc.) who face the need for statistical analysis of experimental results in their activities. It will also be useful for university teachers, graduate students and students.

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7

Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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8

Brown, A. A., and V. V. Petrov. Sums of Independent Random Variables. Springer, 2011.

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9

Sums of Independent Random Variables. Springer, 2011.

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10

Korolev, V. Y., and V. M. Zolotarev. Limit Distributions for Sums of Independent Random Variables. Brill Academic Pub, 2007.

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11

Gnedenko, B. V. Limit distributions for sums of independent random variables. 2nd ed. Wiley, 1994.

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12

M, Lee Lawrence, Nicol David, and United States. National Aeronautics and Space Administration., eds. On the minimum of independent geometrically distributed random variables. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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13

Independent Component Analysis: Algorithms, Applications and Ambiguities. New York, USA: Nova Science Pub Inc., 2018.

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14

Product and Ratio of Generalized Gamma-Ratio Random Variables: Exact and Near-exact distributions - Applications. Lambert Academic Publishing, 2010.

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15

Butyrskiy, Evgeniy. Methods for modeling and estimating random variables and processes. Strategy of the Future, 2020. http://dx.doi.org/10.37468/mon_1850.

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The monograph introduces the basics of theory and practice of mathematical research methods of stochastic systems and processes. It examines the models, methods of describing and forming random events, values and processes, as well as methods of their optimal and suboptimal assessment. The monograph can be useful for a wide range of specialists in various fields of expertise in mathematical and statistical modeling in their research, and can also be used in the learning process to conduct both classroom, and independent theoretical and practical classes with students and masters of St. Petersburg State University engaged in the program «Mathematical modeling» and «Optimal and suboptimal assessment of random processes and systems».

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16

K, Srinivasan S., and Vijayakumar A, eds. Point processes and product densities. New Delhi: Narosa Publ. House, 2003.

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17

Srinivasan, S. K., and A. Vijayakumar. Point Processes and Product Densities. Alpha Science International, 2003.

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18

Meerschaert, Mark M., and Hans-Peter Scheffler. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice (Wiley Series in Probability and Statistics). Wiley-Interscience, 2001.

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19

Comtet1, Alain, and Yves Tourigny2. Impurity models and products of random matrices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0011.

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This is an introduction to the theory of one-dimensional disordered systems and products of random matrices, confined to the 2×2 case. The notion of impurity model—that is, a system in which the interactions are highly localized—links the two themes and enables their study by elementary mathematical tools. After discussing the spectral theory of some impurity models, Furstenberg’s theorem is stated and illustrated, which gives sufficient conditions for the exponential growth of a product of independent, identically distributed matrices.

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20

Bellhouse, David. Probability and Its Application in Britain during the 17th and 18th Centuries. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.5.

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In the 18th and 19th centuries, probability was a part of moral and natural sciences, rather than of mathematics. Still, since Laplace’s 1812 Théorie analytique des probabilités, specific analytic methods of probability aroused the interest of mathematicians, and probability began to develop a purely mathematical quality. In the 20th century the mathematical essence reached full autonomy and constituted “modern” probability. Significant in this development was the gradual introduction of a measure theoretic framework. In this way, the main subfields of modern probability, as axiomatics, weak and strong limit theorems, sequences of non-independent random variables, and stochastic processes, could be integrated into a well-connected complex until World War II.

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21

Scarani, Valerio. Bell Nonlocality. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198788416.001.0001.

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Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.

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22

Adams, Karen Ruth. The Causes of War. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190846626.013.323.

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The scientific study of war is a pressing concern for international politics. Given the destructive nature of war, ordinary citizens and policy makers alike are eager to anticipate if not outright avoid outbreaks of violence. Understanding the causes of war can be a complex process. Scholars of international relations must first define war, and then establish a universe of actors or conflicts in which both war and peace are possible. Next, they must collect data on the incidence of war in the entire universe of cases over a particular period of time, a random sample of relevant cases, a number of representative cases, or a set of cases relevant to independent variables in the theories they are testing. Finally, scholars must use this data to construct quantitative and qualitative tests of hypotheses about why actors fight instead of resolving their differences in other ways and, in particular, why actors initiate wars by launching the first attack. Instead of taking the inductive approach of inventorying the causes of particular wars and then attempting to find general rules, it is necessary for scholars to approach the problem deductively, developing theories about the environment in which states operate, deriving hypotheses about the incidence of war and attack, and using quantitative and qualitative methods to test these hypotheses.

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