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A FUNCTIONAL HUNGARIAN CONSTRUCTION FOR SUMS OF INDEPENDENT RANDOM VARIABLES
Komlos-Major–Tusnády inequality Partial sum process Non-identically distributed variables Function classes Asymptotic equivalence of statistical experiments
2015/8/25
We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions f from a class H, but the supremum over...
Estimating Random Variables from Random Sparse Observations
Discrete random variable random function decoupling principle
2015/8/21
Let X1, . . . ,Xn be a collection of iid discrete random variables, and Y1, . . . , Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a rando...
THE SUBGROUP ALGORITHM FOR GENERATING UNIFORM RANDOM VARIABLES
Subgroup algorithm to generate unified random variable
2015/7/14
THE SUBGROUP ALGORITHM FOR GENERATING UNIFORM RANDOM VARIABLES.
EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNS
Interchangeable Bernoulli random variable KRAWTCHOUCK polynomials Ellen urn
2015/7/7
EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNS。
Inequality for Variance of Weighted Sum of Correlated Random Variables
Variance Covariance Random Variable Chebyshev!ˉs Inequality Correlated Random Variable Positive Semidefinite Matrix Law of Large Numbers
2012/11/23
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also gi...
Explicit Bounds for the Distribution Function of the Sum of Dependent Normally Distributed Random Variables
Explicit Bounds Dependent Normally Distributed Random Variables Distribution Function of the Sum
2011/9/19
Abstract: In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the i...
Tail Asymptotic of Sum and Product of Random Variables with Applications in the Theory of Extremes of Conditionally Gaussian Processes
tail asymptotic Laplace method self-similar processes Gaussian processes locally stationary processes
2011/9/15
Abstract: We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome bu...
Large deviations for truncated heavy-tailed random variables: a boundary case
heavy tails truncation regular variation large deviation
2011/9/6
Abstract: This paper investigates the decay rate of the probability that the row sum of a triangular array of truncated heavy tailed random variables is larger than an integer (k) times the truncating...
A Fock Space Model for Addition and Multiplication of C-free Random Variables
free independence c-free independence creation/annihilation operators
2011/2/22
The paper presents a Fock space model suitable for constructions of c-free algebras. Immediate applications are direct proofs for the properties of the c-free R- and S-transforms.
Entropy power inequality for a family of discrete random variables
Entropy power inequality family of discrete random variables
2011/1/17
It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds wit...
Extend the Borel-Cantelli lemma to sequences of non-independent random variables
Borel-cantelli Lemma Cauchy-schwarz Inequality
2010/9/21
In this paper we discus on the Borel-Cantelli lemma when the condition of independent events is replaced by negative quadrant dependent condition.
On the precise asymptotics in complete moment convergence of moving average processes under NA random variables
Complete convergence Moving average Negatively associated random variable
2010/9/10
On the precise asymptotics in complete moment convergence of moving average processes under NA random variables.
Inequalities on the Variances of Convex Functions of Random Variables
Convex functions variance
2010/1/22
We develop inequalities relating to the variances of convex decreasing functions of random variables using information on the functions and the distribution functions of the random variables.
A Bound on the Deviation Probability for Sums of Non-Negative Random Variables
Deviation bounds Bernstein's inequality Hoeffdings inequality
2008/7/3
A simple bound is presented for the probability that the sum of nonnegative independent random variables is exceeded by its expectation by more than a positive number t. If the variables have the same...
L'Hospital Type Rules for Monotonicity: Applications to Probability Inequalities for Sums of Bounded Random Variables
L'Hospital's Rule Monotonicity Probability inequalities Sums of independent random variables Student's statistic
2008/7/1
This paper continues a series of results begun by a l'Hospital type rule for monotonicity, which is used here to obtain refinements of the Eaton-Pinelis inequalities for sums of bounded independent ra...