Stability Problems for Stochastic Models: Proceedings of the 9th International Seminar held in Varna, Bulgaria, May 13-19, 1985

ISBN-13: 9783540172048 / Angielski / Miękka / 1987 / 224 str.

Vladimir V. Kalashnikov;Boyan Penkov;Vladimir M Zolotarev

Opis

The subject of this book is a new direction in the field ofprobability theory and mathematical statistics which can becalled "stability theory": it deals with evaluating theeffects of perturbing initial probabilistic models andembraces quite varied subtopics: limit theorems, queueingmodels, statistical inference, probability metrics, etc. Thecontributions are original research articles developing newideas and methods of stability analysis.

Spis treści

The estimation of the rate of convergence in the integral limit theorem in the Euclidean motion group.- Contribution to the analytic theory of linear forms of independent random variables.- ?p-strictly stable laws and estimation of their parameters.- The method of metric distances in the problem of estimation of the deviation from the exponential distribution.- The accuracy of the normal approximation to the distribution of the sum of a random number of independent random variables.- Mixtures of probability distributions.- Some limit theorems for summability methods of I.I.D.Random variables.- Properties of mode of spectral positive stable distributions.- Two characterizations using records.- On orthogonal-series estimators for probability distributions.- Estimates of the deviation between the exponential and new classes of bivariate distributions.- On the difference between distributions of sums and maxima.- On the inequalities of Berry-Esseen and V.M. Zolotarev.- Some fixed point theorems probabilistic metric spaces.- The asymptotic bias in a deviation of a location model.- Cramer's decomposition theorem within the continuation of distribution functions.- An asymptotically most Bias-Robust invariant estimator of location.- Characterizing the distributions of the random vectors X 1, X 2, X 3 by the distribution of the statistic (X 1–X 3, X 2–X 3).- On stability estimates of Cramer's theorem.- On the estimation of moments of regenerative cycles in a general closed central-server queueing network.- On F-processes and their applications.- On some properties of ideal metrics of order ?.- On ?-independence of sample mean and sample variance.