description of random process

... Continuing the process of separation for each A− and A+ , we construct a separating tree of subsets of A A tree of nonempty subsets of a set A is a finite collection T of subsets of A such that ... Gaussian processes A quantitative version of Theorem 1.1 is the following bound on Gaussian processes indexed by F in terms of the combinatorial dimension of F COMBINATORICS OF RANDOM PROCESSES ... translates of L and then cover the intersection of K with each translate by appropriate translates of D 635 COMBINATORICS OF RANDOM PROCESSES It will be easier to work with the “covering” analog of...

Ngày tải lên: 22/03/2014, 20:20

... problem of systems more complex, even lose its essence Disregarding the characteristics of dead time delay of an object is one of the reasons that leads to a great number of research directions of ... the behaviour of output response and is equal to the degree of the asymptote of output response q = if the asymptote of output response is horizontal asymptote q = if the asymptote of output response ... optimization problems, Proceeding of NCST of VietNam, No (1992) 53 [8] Nguyen Van Manh, Methods Optimization of Control System for Uncertaint Processes, Dissertation of Science Doctor Moscow Power...

Ngày tải lên: 28/03/2014, 13:20

... problem of systems more complex, even lose its essence Disregarding the characteristics of dead time delay of an object is one of the reasons that leads to a great number of research directions of ... the behaviour of output response and is equal to the degree of the asymptote of output response q = if the asymptote of output response is horizontal asymptote q = if the asymptote of output response ... optimization problems, Proceeding of NCST of VietNam, No (1992) 53 [8] Nguyen Van Manh, Methods Optimization of Control System for Uncertaint Processes, Dissertation of Science Doctor Moscow Power...

Ngày tải lên: 28/03/2014, 13:20

... containing a number of balls of different types The set This is a de facto observation, not a definition of reinforced processes Robin Pemantle /Random processes with reinforcement of types may be ... constant Proof: Let j ≤ k be such that j out of 2k + neighbors of type is sufficient to make strategy optimal Once there are j consecutive players of type 1, the size of the interval of players of type ... surely to the zero set of F Proof: consider the sub-intervals [a, b] of intervals (a0 , b0 ) on which F > δ or F < −δ Countably many of these cover the complement of the zero set of F and each is...

Ngày tải lên: 11/11/2015, 04:36

... Convergence of a Sequence of Random Variables 2.1 Four definitions of convergence of random variables 2.2 Cauchy criteria for convergence of random variables 2.3 Limit theorems for sequences of independent ... Basic Calculus of Random Processes 5.1 Continuity of random processes 5.2 Differentiation of random processes 5.3 Integration of random process 5.4 Ergodicity 5.5 Complexification, ... 45 45 46 53 55 56 60 Random Processes 4.1 Definition of a random process 4.2 Random walks and gambler’s ruin 4.3 Processes with independent increments...

Ngày tải lên: 12/11/2015, 01:03

... 62 Extremal processes 5.1 Point processes 5.2 Laplace functionals 5.3 Poisson point processes 5.4 Convergence of point processes 5.5 Point processes of extremes 64 64 67 68 70 76 Processes with ... data (which could be the observation of N of these random variables) a statistical model of this process, i.e., a probability distribution of the infinite random sequence {Xi }i∈Z Usually, this ... size of the jump of F at x Thus, (1.61) says that the size of jumps of F should diminish faster, as x approaches the upper boundary of the support of F , than the total mass beyond x Proof Assume...

Ngày tải lên: 12/11/2015, 02:03

... Laws of Large Numbers and the Central Limit Theorem Solved Problems Chapter Random Processes 5.1 Introduction 5.2 Random Processes 5.3 Characterization of Random Processes 5.4 Classification of Random ... Chapter Functions of Random Variables, Expectation, Limit Theorems 4.1 Introduction 4.2 Functions of One Random Variable 4.3 Functions of Two Random Variables 4.4 Functions of n Random Variables ... Schaum's Outline of Theory and Problems of Probability, Random Variables, and Random Processes Hwei P Hsu, Ph.D Professor of Electrical Engineering Fairleigh Dickinson University Start of Citation[PU]McGraw-Hill...

Ngày tải lên: 31/03/2014, 16:25

... family of random processes”) is a fixed subset of RL , for some fixed integer L For a fixed q ∈ Q, we think of {xq (t), t ∈ Z} as a random process in discrete time, and we assume that this process ... for the family of enveloped chirp processes 3.3 A Family of Chirp Processes In this example, we will study measurements of heart rate variability (HRV), [16] Such measurements are often modeled ... 19] Conclusions and Final Remarks A non-parametric estimate of the covariance function of a random process is often obtained by the use of a kernel function Different kernel functions have been proposed,...

Ngày tải lên: 21/06/2014, 07:20

... coordinates of branch point and of final point of virtual segments; and 5) the rank of branch point a Final data structure: ments resorting root seg- Growth and branching pattern analysis Statistical processing ... Statistical processing of computed coordinates allows the calculation of some root architectural characteristics Each root is specified in terms of elongation and ramification Some of them are time-indepen- ... (e.g., number of root, number of parent root, root order, branch angle, Dbase, interbranch distance and time of emergence); the others evolve with time (e.g., root elongation or velocity of lateral...

Ngày tải lên: 09/08/2014, 02:21

... mixed The simultaneous consideration of more than one random variable is often necessary or useful In the case of two, the probability of the occurrence of pairs of values in a given range is prescribed ... I t is of frequent importance to find the expectation of a function of a random variable If Y is defined to be some function of the random variable X, say, Y = g(X), then Y is itself a random ... the expectation of the product of random variables is equal to the product of the expectations, if the variables are independent It is also true that the variance of the sum of random variables...

Ngày tải lên: 15/10/2012, 15:43

... stationary if the roots of the z polynomial lie inside a circle of radius one An AR process is a finite linear combination of its past values and the current value of a random process The present ... acvs for an AR process dies out gradually with lag and never reaches zero 2.5 Moving Average Process An MA process is a linear combination of present and past values of a noise process with a ... considering stationary processes: one whose statistical properties are independent of time, or a physical system which is steady state If {Xt } is a result of a stationary process, then each element...

Ngày tải lên: 15/10/2012, 15:43

... stationary if the roots of the z polynomial lie inside a circle of radius one An AR process is a finite linear combination of its past values and the current value of a random process The present ... acvs for an AR process dies out gradually with lag and never reaches zero 2.5 Moving Average Process An MA process is a linear combination of present and past values of a noise process with a ... considering stationary processes: one whose statistical properties are independent of time, or a physical system which is steady state If {Xt } is a result of a stationary process, then each element...

Ngày tải lên: 16/10/2012, 09:09

... sums of integer powers of the values Best known is the mean of the values x1 , , xN , x= N N xj (14.1.1) j=1 which estimates the value around which central clustering occurs Note the use of ... 1974, Applied Statistics: Analysis of Variance and Regression (New York: Wiley) 14.1 Moments of a Distribution: Mean, Variance, Skewness, and So Forth When a set of values has a sufficiently strong ... tendency, the moments of a distribution, the median and mode In §14.2 we learn to test whether different data sets are drawn from distributions with different values of these measures of central tendency...

Ngày tải lên: 20/10/2013, 17:15

... significance of a difference of means is not the number of standard deviations that they are apart, but the number of so-called standard errors that they are apart The standard error of a set of values ... definitions into sums of various powers of the data, e.g., the familiar    N  x2  − N x2  ≈ x2 − x2 (14.1.7) Var(x1 xN ) = j N −1 614 Chapter 14 Statistical Description of Data Semi-Invariants ... the first moment of the tails is large; it is easy to construct examples where the first moment of the tails is large even though their area is negligible To find the median of a set of values, one...

Ngày tải lên: 24/10/2013, 15:15

... *prob=betai(0.5*df,0.5,df/(df+(*t)*(*t))); Degrees of freedom Pooled variance See equation (6.4.9) } which makes use of the following routine for computing the mean and variance of a set of numbers, Sample page from ... of research: Are the visible stars distributed uniformly in the sky? (That is, is the distribution of stars as a function of declination — position in the sky — the same as the distribution of ... function of declination?) Are educational patterns the same in Brooklyn as in the Bronx? (That is, are the distributions of people as a function of last-grade-attended the same?) Do two brands of fluorescent...

Ngày tải lên: 24/10/2013, 15:15

... then the number of degrees of freedom is NB − If he takes his data to be all the birds he saw on a random sample of days, the same days in each year, then the number of degrees of freedom is NB ... collected in such a way that the sum of the Ri ’s is necessarily equal to the sum of Si ’s, then the number of degrees of freedom is equal to one less than the number of bins, NB − (that is, knstrn ... of the squares of ν random normal variables of unit variance (and zero mean) will be greater than χ2 The terms in the sum (14.3.1) are not individually normal However, if either the number of...

Ngày tải lên: 28/10/2013, 22:15

... Table Analysis of Two Distributions female # of red males N11 # of green males N12 # of males N1⋅ # of red females N21 # of green females N22 # of females N2⋅ # of red N ⋅1 ... association In this case, the probability of a particular value of x given a particular value of y should be the same as the probability of that value of x regardless of y Therefore, in the null hypothesis, ... The number of degrees of freedom is equal to the number of entries in the table (product of its row size and column size) minus the number of constraints that have arisen from our use of the data...

Ngày tải lên: 28/10/2013, 22:15

... respectively, the number of data points in the measurement of r1 and r2 All of the significances above are two-sided If you wish to disprove the null hypothesis in favor of a one-sided hypothesis, ... concept of nonparametric correlation is this: If we replace the value of each xi by the value of its rank among all the other xi ’s in the sample, that is, 1, 2, 3, , N , then the resulting list of ... detecting correlation between uniform sets of integers between and N , keeping in mind the possibility of ties in the ranks There is, of course, some loss of information in replacing the original...

Ngày tải lên: 07/11/2013, 19:15