Deviation Probabilities For Sums Research Articles

Small Deviation Probabilities of a Sum of Independent Positive Random Variables, the Common Distribution of Which Decreases at Zero Not Faster Than Exponential Function

We investigate small deviation probabilities of the cumulative sum of independent positive random variables, the common distribution of which decreases at zero not faster than exponential function.

Small Deviation Probabilities for Sums of Independent Positive Random Variables with a Distribution that Slowly Varies at Zero

In the note, we study small deviation probabilities for sums of independent, identically distributed positive random variables whose distribution function is slowly varying at zero. Bibliography: 5 titles.

Small deviation probabilities for sums of independent positive random variables whose density has a power decay at zero

In this note, we study small deviation probabilities of a sum of i.i.d. positive random variables whose density has a power decay at zero. Bibliography: 3 titles.

Lower estimations of the deviation probabilities for sums of Bernoulli random variables

We obtain lower bilateral and unilateral estimations of the deviation probability of the arithmetic mean of independent Bernoulli random variables from mathematical expectation.

Probabilities of Large Deviations of Type II Errors for Tests of Kolmogorov and Omega-Square Types

For the Kolmogorov and omega-square tests, strong asymptotics for large deviations of type II error probabilities are obtained in the case of “least favorable alternatives.” Using these asymptotics, type II error probabilities for any sequence of alternatives can readily be estimated. The proofs are based on an exact asymptotic of large deviation probabilities for Gaussian measures in a Hilbert space and on a theorem on large deviation probabilities for sums of independent random vectors in a Banach space. Bibliography: 22 titles.

Estimate of Distributions of Sums of Independent Random Variables

We investigate necessary and sufficient conditions under which one estimate of exponential type is valid for large deviation probabilities of sums of independent identically distributed random variables. Bibliography: 3 titles.

An asymptotic formula for the Bayes risk in discriminating between two Markov chains

The problem of discriminating between two Markov chains is considered. It is assumed that the common state space of the chains is finite and all the finite dimensional distributions are mutually absolutely continuous. The Bayes risk is expressed through large deviation probabilities for sums of random variables defined on an auxiliary Markov chain. The proofs are based on a large deviation theorem recently established by Z. Szewczak.

An Inequality for Large Deviation Probabilities of Sums of Bounded i.i.d. Random Variables

We provide precise bounds for tail probabilities, say ℙ{M n ⩾ x}, of sums M n of bounded i.i.d. random variables. The bounds are expressed through tail probabilities of sums of i.i.d. Bernoulli random variables. In other words, we show that the tails are sub-Bernoullian. Sub-Bernoullian tails are dominated by Gaussian tails. Possible extensions of the methods are discussed.

Large deviation probabilities for sums of lattice random vectors with heavy-tailed distribution

Large deviation probabilities for sums of lattice random vectors with heavy-tailed distribution

Large deviation probabilities of sums of independent random vectors for certain classes of sets

Large deviation probabilities of sums of independent random vectors for certain classes of sets

On Moderate Deviation Probabilities for Sums of Independent Random Variables

On Moderate Deviation Probabilities for Sums of Independent Random Variables

On Large Deviation Probabilities for Sums of Independent Random Vectors

On Large Deviation Probabilities for Sums of Independent Random Vectors

On large deviation probabilities for sums of random variables which are attracted to the normal law

For the sequence {xn of independent identically distributed random variable satisrying P{x1>x} x L(x) and P{-x1>x} x L1(x),where p≥2 and L,L1 are functions of slow variation such that L1(x)/L(x)−p as x→∞,it is shown that P{Sn>>ta}∽np{X1>>tn}for certain sequences tn;here

On Large Deviation Probabilities for Sums of Random Variables Which are Attracted to the Normal Law

On Large Deviation Probabilities for Sums of Random Variables Which are Attracted to the Normal Law