Distributed random

Let us consider the composed random variable η = k=1 ξk , where ξ1 , ξ2 , ... are independent identically distributed random variables and ν is a positive value random, independent of all ξk . In [1] and [2], we gave some the stabilities of the distribution function of η in the following sense: the small changes in the distribution function of ξ k only lead to the small changes in the distribution function of η. In the paper, we investigate the distribution function of η when we have the small changes of the distribution of ν. ...
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For many random variables, the probability distribution is a specific bellshaped curve, called the normal curve, or Gaussian curve. This is the most common and useful distribution in statistics. 1) Standard normal distribution The standard normal distribution has the probability density function as follows:
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Chapter 3 REFINEMENTS OF THE LIMIT THEOREMS FOR NORMAL CONVERGENCE § 1 . Introduction In this chapter we consider a sequence X 1 , X2 , . . . of independent, identically distributed random variables belonging to the domain of attraction of the normal law. As shown in § 2 .6, the X; necessarily have a finite variance a 2 .
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Chapter 7 RICHTER'S LOCAL THEOREMS AND BERNSTEIN'S INEQUALITY 1 . Statement of the theorems The theorems of this chapter do not have a collective character, and are related to Theorem 6 .1.1 . We shall consider a sequence of independent, identically distributed random variables XX
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Chapter 12 WIDE MONOMIAL ZONES OF INTEGRAL NORMAL ATTRACTION 1 . Formulation In this chapter, as before, we study the independent, identixally distributed random variables X1, X2, . . . with E (Xi) = 0, V (Xl) = 1 . We shall study the zone [0, n"] where a 6 ; we recall that this is said to be a zone of normal attraction if,
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Chapter 4 LOCAL LIMIT THEOREMS § 1. Formulation of the problem Suppose that the independent, identically distributed random variables X1 , X2 ,. . . . have a lattice distribution with interval h, so that the sum Zn = X1 + X2 + . . . + X„ takes values in the arithmetic progression {na + kh ; k = 0, ± 1, . . . } .
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Chapter 6 LIMIT THEOREMS FOR LARGE DEVIATIONS § 1 . Introduction and examples In this and succeeding chapters we shall examine the simplest problems in the theory of large deviations . Let X1 , X2 ,. . . be independent, identically distributed random variables, with E(X1) = 0
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Let A be an n × n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A−1 does not exceed Cn3/2 with probability close to 1. 1. Introduction Let A be an n × n matrix, whose entries are independent, identically distributed random variables. The spectral properties of such matrices, in particular invertibility, have been extensively studied (see, e.g. [M] and the survey [DS]).
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This chapter is of an introductory nature, its purpose being to indicate some concepts and results from the theory of probability which are used in later chapters . Most of these are contained in Chapters 19 of Gnedenko [47], and will therefore be cited without proof. The first section is somewhat isolated, and contains a series of results from the foundations of the theory of probability. A detailed account may be found in [76], or in Chapter I of [31] . Some of these will not be needed in the first part of the book, in which attention is confined to independent random variables ....
0p denngudo 21062012 23 5 Download

Tham khảo sách 'probability examples c3 random variables ii', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả
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Tham khảo sách 'probability examples c4 random variables iii', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả
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This paper presents an attempt at building a large scale distributed composite language model that simultaneously accounts for local word lexical information, midrange sentence syntactic structure, and longspan document semantic content under a directed Markov random ﬁeld paradigm.
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Frequency distribution models tuned to words and other linguistic events can predict the number of distinct types and their frequency distribution in samples of arbitrary sizes. We conduct, for the ﬁrst time, a rigorous evaluation of these models based on crossvalidation and separation of training and test data. Our experiments reveal that the prediction accuracy of the models is marred by serious overﬁtting problems, due to violations of the random sampling assumption in corpus data. We then propose a simple preprocessing method to alleviate such nonrandomness problems. ...
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Recent work on Conditional Random Fields (CRFs) has demonstrated the need for regularisation to counter the tendency of these models to overﬁt. The standard approach to regularising CRFs involves a prior distribution over the model parameters, typically requiring search over a hyperparameter space. In this paper we address the overﬁtting problem from a different perspective, by factoring the CRF distribution into a weighted product of individual “expert” CRF distributions. We call this model a logarithmic opinion pool (LOP) of CRFs (LOPCRFs).
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We describe a novel method that extracts paraphrases from a bitext, for both the source and target languages. In order to reduce the search space, we decompose the phrasetable into subphrasetables and construct separate clusters for source and target phrases. We convert the clusters into graphs, add smoothing/syntacticinformationcarrier vertices, and compute the similarity between phrases with a random walkbased measure, the commute time.
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Lecture Quantiative methods for bussiness  Chapter 3A presents probability distributions. This chapter includes the following content: Random variables, discrete probability distributions, binomial probability distribution, poisson probability distribution.
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We propose a succinct randomized language model which employs a perfect hash function to encode ﬁngerprints of ngrams and their associated probabilities, backoff weights, or other parameters. The scheme can represent any standard ngram model and is easily combined with existing model reduction techniques such as entropypruning. We demonstrate the spacesavings of the scheme via machine translation experiments within a distributed language modeling framework. h
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This paper presents a semisupervised training method for linearchain conditional random ﬁelds that makes use of labeled features rather than labeled instances. This is accomplished by using generalized expectation criteria to express a preference for parameter settings in which the model’s distribution on unlabeled data matches a target distribution. We induce target conditional probability distributions of labels given features from both annotated feature occurrences in context and adhoc feature majority label assignment. ...
9p hongphan_1 15042013 19 1 Download

In this paper, we present an automated, quantitative, knowledgepoor method to evaluate the randomness of a collection of documents (corpus), with respect to a number of biased partitions. The method is based on the comparison of the word frequency distribution of the target corpus to word frequency distributions from corpora built in deliberately biased ways. We apply the method to the task of building a corpus via queries to Google.
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Lectures "Applied statistics for business  Chapter 5: Discrete probability distributions" provides students with the knowledge: Random variables, developing discrete probability distributions, expected value and variance, expected value and variance financial portfolios,... Invite you to refer to the disclosures.
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