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Probability and statistics

About: Probability and statistics is a research topic. Over the lifetime, 3403 publications have been published within this topic receiving 214735 citations.


Papers
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Book
01 Jan 1988

1,522 citations

Book
01 Jan 1994
TL;DR: In this paper, the authors provide a study of applications of dependence in probability and statistics, focusing on mixing, which is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space.
Abstract: Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. It provides an important tool of analysis for random fields, Markov processes and central limit theorems as well as being a topic of current research interest in its own right. The aim of this monograph is to provide a study of applications of dependence in probability and statistics. It is divided into two parts, the first covering the definitions and probabilistic properties of mixing theory, the second describing mixing properties of classical processes and random fields as well as providing a detailed study of linear and Gaussian fields.

1,487 citations

Journal ArticleDOI
TL;DR: In this paper, a new theory for the analysis of games with incomplete information has been described, and it has been shown that in consistent games, where a basic probability distribution exists, it is essentially unique.
Abstract: Parts I and II of this paper have described a new theory for the analysis of games with incomplete information. Two cases have been distinguished: consistent games in which there exists some basic probability distribution from which the players' subjective probability distributions can be derived as conditional probability distributions; and inconsistent games in which no such basic probability distribution exists. Part III will now show that in consistent games, where a basic probability distribution exists, it is essentially unique. It will also be argued that, in the absence of special reasons to the contrary, one should try to analyze any given game situation with incomplete information in terms of a consistent-game model. However, it will be shown that our theory can be extended also to inconsistent games, in case the situation does require the use of an inconsistent-game model.

1,413 citations

Journal ArticleDOI
TL;DR: This paper presents a meta-modelling framework for estimating the probabilities of different types of population sizes using a simple linear Regression model, and some examples show how this model can be modified to accommodate diverse population sizes.

1,406 citations

Book
01 Jan 1946
TL;DR: In this article, Cramer joins two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probablists transformed the classical calculus of probability into a rigorous and purely mathematical theory.
Abstract: In this text about statistical mathematical theory, Harald Cramer joins two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probablists transformed the classical calculus of probability into a rigorous and purely mathematical theory. The result of Cramer's work is an exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow. The first part of the book 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.

1,322 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202246
202170
2020150
2019147
2018138