Journal ArticleDOI
Convergent and Asymptotic Expansions for Probability Distributions
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This article is published in Theory of Probability and Its Applications.The article was published on 1967-01-01. It has received 14 citations till now. The article focuses on the topics: Asymptotic analysis & Convolution of probability distributions.read more
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Book ChapterDOI
Limit Theorems on Large Deviations
L. Saulis,V. Statulevičius +1 more
TL;DR: In this paper, the authors deal with limit theorems on large deviations on independent random variables and apply analytic tools that are applicable to this case that allow one to understand the general behavior of the probabilities of large deviations.
Journal ArticleDOI
A Comparison of Some Approximate Confidence Intervals for the Binomial Parameter
TL;DR: In this paper, the authors compared two confidence intervals for the binomial parameter that are frequently recommended for large samples and showed that one of them, which is in fact less popular in the literature, enjoys certain advantages over the other one.
Journal ArticleDOI
Negative binomial processes
TL;DR: In this paper, the authors studied the distribution of the number of points of a k-dimensional negative binomial process in a compact subset of Rk, and in particular in the case where the underlying Gaussian processes are independent Ornstein-Uhlenbeck processes when more detailed results may be obtained.
Journal ArticleDOI
Some analogs of the berry-esséen bound for first-order chebyshev-edgeworth expansions
V. Dobrić,B. K. Ghosh +1 more
TL;DR: In this paper, the authors consider the distribution funct ion of the stajidardized sum of an arb i t rary number of independent and identically disordered variables and give a uniform upper bound for the absolute difference between this distribution and the standard normal distribution.
Journal ArticleDOI
Asymptotic Expansion of the Distribution Density Function for the Sum of Random Variables in the Series Scheme in Large Deviation Zones
D. Deltuvienė,L. Saulis +1 more
TL;DR: In this paper, the authors obtained asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme.