The classical Fatou inequality for non-negative measurable functions is intimately connected with problems of convergence of random variables (r.v.). The present paper focuses on the study of a modified form of the Fatou inequality which has important applications in the theory of convergence of r.v. We formulate our results in the language of probability.

Topics: DTIC Archive, Dvoretzky,A, STANFORD UNIV CA DEPT OF STATISTICS, *Inequalities, Convergence, Random...

Wyners common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, and also confined to, several existing interpretations in various source coding problems. This paper attempts to expand its practical significance by providing a new operational interpretation. In the context of the GrayWyner network, it is established that Wyners common information has a new lossy source coding interpretation. Specifically, it is...

Topics: DTIC Archive, Liu,Wei, Syracuse University Syracuse United States, information theory, random...

In this paper we obtain central limit theorems for some dependent random variables which are used to describe the distribution of magnetic spins present in a ferromagnet crystal. A ferromagnet crystal consists of a large number of sites. At site i there is some amount of magnetic spin present. The magnetic spin present at any site interacts with the magnetic spins at its neighboring sites and hence gives rise to some dependency among the magnetic spin present.

Topics: DTIC Archive, Chaganty,Narasinga Rao, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS,...

Topics: DTIC Archive, Rudolph,Daniel, STANFORD UNIV CA DEPT OF STATISTICS, *ORDER STATISTICS, RANDOM...

In this paper, refined large deviation asymptotics are derived for the classical occupancy problem. The asymptotics are established for a sequential filling experiment and an occupancy experiment. In the first case, the random variable of interest is the number of balls required to fill a given fraction of the urns, while in the second a fixed number of balls are thrown and random variable is the fraction of nonempty urns.

Topics: DTIC Archive, Dupuis, Paul, BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS, *ASYMPTOTIC...

Simple linear rank statistics arise in a variety of situations, particularly in the problem of testing the equality of two or more distributions by non-parametric tests. While the asymptotic distributions of simple linear rank statistics have been studied extensively (see, e.g., Hajek and Sidak (1967) ), investigations concerning their large deviation properties have been made only recently (Stone (1967, 1968, 1969) and Woodworth (1970)). In this paper the authors study the rates of convergence...

Topics: DTIC Archive, Clickner, Robert P., Sethuraman, Jayaram, ARMY RESEARCH OFFICE RESEARCH TRIANGLEPARK...

In this article we obtain central limit theorems for some dependent random variables which are used to describe the distribution of magnetic spins present in a ferromagnet crystal. A ferromagnet crystal consists of a large number of sites. At site 1 there is some amount of magnetic spins present. The magnetic spin present at any site interacts with the magnetic spins at its neighboring sites and hence gives rise to some dependency among the magnetic spin present.

Topics: DTIC Archive, Chaganty,N R, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *CRYSTALS,...

Topics: DTIC Archive, Wahba,Grace, WISCONSIN UNIV-MADISON DEPT OF STATISTICS, *SPLINES(GEOMETRY), RANDOM...

Suppression produced among combatants exposed to mixed, nonuniform fires is given an operational explication through a 'single-round period of suppressive effect' which is permitted to have a random duration that may stochastically depend upon miss-distance. Explicit formulas are derived for the expected duration of periods of suppression and for expected detection times when the underlying search activity is suspended during periods of suppression. Suppression thus represented as a hiatus in...

Topics: DTIC Archive, Horrigan, Timothy J., HORRIGAN ANALYTICS CHICAGO IL, *WARFARE, *SUPPRESSION,...

Topics: DTIC Archive, Holst,Lars, STANFORD UNIV CA DEPT OF STATISTICS, *STATISTICAL FUNCTIONS, RANDOM...

Maximum likelihood estimation of the parameters lambda and mu of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The related problem of estimation from the discrete skeleton of the process is also discussed.

Topics: DTIC Archive, Keiding, Niels, STANFORD UNIV CA DEPT OF STATISTICS, *STOCHASTIC PROCESSES,...

This document presents some theorems on the strong law for the mixing sequence which is not necessarily stationary, and the mixing coefficient involving only a pair of variables in the sequence. Keywords: Large numbers, Random variables, Autoregression models.

Topics: DTIC Archive, Chen, Xiru, PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS, *COEFFICIENTS,...

This paper presents a survey of large deviation local limit theorems for random vectors. The authors then establish a more extensive large deviation local limit theorem that requires somewhat weaker conditions even in the special cases proved earlier. (Author)

Topics: DTIC Archive, Chaganty,Narasinga R, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *PROBABILITY...

In another document Shepp has used certain definitions of unimodality and peakedness to show that if F and G are symmetric unimodal and F is less peaked than G, then the recurrence of F implies the recurrence of G. This paper extends Shepp's result to a wider class of symmetric and unimodal distributions.

Topics: DTIC Archive, Dharmadhikari,S W, FLORIDA STATE UNIV TALLAHASSEE, *Distribution functions, Symmetry,...

General properties of growth rates of moment sequences of nonnegative random variables are presented. Then asymptotic results on moment sequences are derived for two classes of distribution functions. Explicitly, let a monotone be increasing twice differentiable regularly varying function at infinity. A second class of distribution functions is defined. Finally, several examples are given to illustrate the possible different asymptotic growth rates of moments.

Topics: DTIC Archive, Harkness,William L, STANFORD UNIV CA DEPT OF STATISTICS, *SEQUENCES(MATHEMATICS),...

The process be described in this report can be determined by sampling at fixed intervals nh, n = 0, + or - 1,... , h = pi/alpha 0. A corresponding result is also obtained for a more general Cramer class. To carry out this analysis, it is necessary to use the properties of bimeasures. Some aspects of the bimeasure theory and its distinction from the Lebesgue theory are included. This is used essentially for the analysis of harmonizable processes, and has independent interest.

Topics: DTIC Archive, Chang,Derek K, CALIFORNIA UNIV RIVERSIDE DEPT OF MATHEMATICS, *THEOREMS, *HARMONIC...

The main objective of the present note is to solve a problem proposed by Weide (1978) concerning the complete convergence of certain random variables associated with Karp's probabilistic analysis of the traveling salesman problem (Karp (1976), (1977)).

Topics: DTIC Archive, Steele,J Micheal, STANFORD UNIV CA DEPT OF STATISTICS, *ALGORITHMS, RANDOM VARIABLES,...

Let X sub t be a discrete parameter time series generated by a model such that E(X sub t) is the sum of a finite number of simple harmonic terms of the form A cos omega t + B sin omega t, and X sub t - E(X sub t) is a moving average of independently identically distributed random variables epsilon sub t, whose weights g sub u (theta) are specified functions of a vector-valued parameter theta. In 1952 P. Whittle proposed an approximate least-squares method of simultaneously estimating theta and...

Topics: DTIC Archive, Walker, A M, STANFORD UNIV CA DEPT OF STATISTICS, *INFORMATION THEORY, *TIME SERIES...

The report considers a generalization of the repairman models treated in a previous report. Here the system studied consists of n operating units, M(n) spare units, and two repair facilities. The operating units are subject to failures of two types: minor and major. Minor failures are sent to a local repair facility and major failures to a central repair facility. Once a unit is repaired it is returned to the spare pool is n units are operating, otherwise it goes directly into operation. The...

Topics: DTIC Archive, Iglehart, Donald L, CONTROL ANALYSIS CORP PALO ALTO CA, *MAINTENANCE, *STOCHASTIC...

The generalized lattice point (GLP) problem provides a formulation that accommodates a variety of discrete alternative problems. In the paper the authors show how to substantially strengthen the convexity cuts for the GLP problem. The new cuts are based on the identification of synthesized lattice point conditions to replace those that ordinarily define the cut. The synthesized conditions give an alternative set of hyperplanes that enlarge the convex set, thus allowing the cut to be shifted...

Topics: DTIC Archive, Glover, Fred, TEXAS UNIV AT AUSTIN CENTER FOR CYBERNETIC STUDIES, *LINEAR...

This document discusses an arbitrary sequence of non-lattice random variables and another sequence of positive random variables. Assume that the sequences are independent. This paper obtains asymptotic expression for the density function of the ratio statistic R sub n = T sub n/S sub n based on simple conditions on the moment generating functions of T sub n and S sub n. When S sub n = n, our main result reduces to that of Chaganty and Sethuraman. We also obtain analogous results when T sub n...

Topics: DTIC Archive, Chaganty, Narasinga R, OLD DOMINION UNIV NORFOLK VA, *RANDOM VARIABLES, *STATISTICAL...

A statistical procedure is asymptotically robust if its large-sample properties hold under conditions more general than the conditions under which the procedure is derived. The justification of such procedures is often based directly or indirectly on a central limit theorem. In this paper Lindeberg-type conditions are utilized to establish asymptotic normality of sample regression and autoregression coefficients.

Topics: DTIC Archive, Anderson, T W, STANFORD UNIV CA DEPT OF STATISTICS, *REGRESSION ANALYSIS, *ASYMPTOTIC...

Most vulnerable area (A sub v) analyses consider component probability of kill given a hit, P(K/H), to be a point estimate with no variance. This report presents statistical methods for calculating assurance limits for (A sub v) assuming P(K/H)'s are not known with certainty . Normal approximation and Monte Carlo techniques are presented. The accuracy of these techniques is determined analytically for a target with a small number of critical components and extended to a larger number of...

Topics: DTIC Archive, Kemp, Jerry, Montgomery, David, Papke, Norman, NAVAL WEAPONS SUPPORT CENTER CRANE IN,...

Topics: DTIC Archive, Korwar,Ramesh M, MASSACHUSETTS UNIV AMHERST DEPT OF MATHEMATICS AND STATISTICS,...

An earlier, referenced report considered the existence of trend-free block designs and gave some general results for general block designs and some special results for complete block designs. This report presents a new existence theorem that is sufficiently general to cover broad classes of incomplete block designs and suggests a design construction method. Suppose that a common trend affecting treatment responses exists over the plots within blocks of a block design with usual design...

Topics: DTIC Archive, Yeh,Ching-Ming, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS,...

The object of this paper is to derive the asymptotic distributions of simple linear signed rank statistic considered by Hajek (1968) and Huskova (1970) for the case when the score generating function is discontinuous.

Topics: DTIC Archive, Puri,Madan L, INDIANA UNIV AT BLOOMINGTON DEPT OF MATHEMATICS, *ASYMPTOTIC NORMALITY,...

Given n observations from each of k populations whose distributions differ by a location parameter, the value of the largest parameter is to be estimated using the largest value of the k sample means. It is desired to design a sampling rule which guarantees that the Mean Squared Error (M.S.E.) of the estimate does not exceed a given bound when the distributions have a common but unknown scale parameter. A sequential sampling scheme is devised based on an estimate of the scale parameter and a...

Topics: DTIC Archive, Blumenthal, Saul, CORNELL UNIV ITHACA NY DEPT OF OPERATIONS RESEARCH, *SEQUENTIAL...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

Sufficient conditions for consistency of a nonparametric maximum likelihood estimate are given which are applicable to those problems where a class of distribution functions is specified only in terms of its graphs. Consistency is proven and applications are given.

Topics: DTIC Archive, Crawford, Gordon B, BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH...

Renewal theorems are obtained for a class of perturbed arithmetic random walks. An application to the study of fixed-width confidence intervals is discussed. (Author)

Topics: DTIC Archive, Lalley,Steve, STANFORD UNIV CA DEPT OF STATISTICS, *SEQUENTIAL ANALYSIS, RANDOM...

Let X sub (1) ... X sub (n) be the order statistics of a random sample from a population with density f and distribution function F such that F(0) = 0. Let q(t) = f(t)/(1 - F(t)) be the failure rate of F. In testing H sub o: q(t) = lambda vs. H sub l: q(t) vertical arrow, Proschan and Pyke (Vth Berk. Symp.) considered certain statistics based on R sub l, ..., R sub n, the ranks of the normalized sample spacings D sub i = (n - i + l) (X sub (i) - X sub (i-l)), 1 = or i = or n, X sub (o) = 0....

Topics: DTIC Archive, Bickel, Peter J, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *SAMPLING,...

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, MAXIMUM LIKELIHOOD ESTIMATES, STOCHASTIC...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

The distribution under alternatives of a simple linear rank statistic S sub n is governed by the following entities: a set of regression constants (series C from ml to nn), scores (series a from nl to nn) and distribution functions (series F from nl to nn). One usually assumes the scores to be generated by a known function phi.

Topics: DTIC Archive, Rajaram,Navaratna S, INDIANA UNIV BLOOMINGTON DEPT OF MATHEMATICS, *STOCHASTIC...

Define F (subscript s) G F (subscript r) G if F and G have the same median, say the origin and G (superscript -1) F(x) is concave-convex about the origin (G (superscript -1) F(x)/x is increasing (decreasing) in x positive (negative)). Conservative tolerance limits are derived for distributions which are s-ordered with respect to the Laplace distribution. These are especially reasonable for mensuration data. In addition, many inequalities concerning combinations of order statistics are obtained....

Topics: DTIC Archive, Lawrence, Michael J, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER,...

In this paper, we present conditions on the likelihood function and on the prior distribution which permit us to assess the effect of the sample on the posterior distribution. Our work is inspired by Whitt (1979) J. Amer. Statist. Assoc. 74, and is based on the notion of multivariate totally positive functions introduced by Karlin and Rinott (1980), unpublished report. (Author)

Topics: DTIC Archive, Fahmy,Salwa, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *MULTIVARIATE...

The relationship of minimum distance (MD) estimation to other methods of estimation is considered. M-estimation is viewed as a special case, with interesting interpretations in terms of the defining - function as related to components of goodness-of-fit statistics and modified Fourier approximations to the efficient score. Applications to the composite and simple goodness-of-fit problems are considered. (Author)

Topics: DTIC Archive, Parr,William C, SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS, *STATISTICAL...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

Necessary and sufficient conditions for the functional central limit theorem for a double array of random variables are sought. It is argued that this is a martingale problem only if the variables truncated at some fixed point c are asymptotically a martingale difference array. Under this hypothesis, necessary and sufficient conditions for convergence in distribution to a Brownian motion are obtained when the normalization is given (i) by the sums of squares of the variables, (ii) by the...

Topics: DTIC Archive, Rootzen, Holger, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *DISTRIBUTION...

In this paper we propose and develop techniques for solving structured, large-scale convex programming problems. The procedure is a combination of a decomposition technique of Dantzig-Wolfe type and the proximal point method. The proximal point method is used to overcome the drawbacks of the decomposition technique. The procedure is then used to solve block angular linear programming problems. By exploiting the linearity of the problem we have several variants of the procedure. (Author)

Topics: DTIC Archive, Ha,Cu Duong, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *LINEAR PROGRAMMING,...

Simple methods of construction lead to families of PBIB designs with triangular and L sub 2 schemes. The construction can be carried out in a s dimensions to obtain PBOB designs with at most s associate classes. A family of such PBIB designs (indexed by the block size) has the desirable statistical property that a pair of distinct varieties appears in at most one block. (Author)

Topics: DTIC Archive, Constantine,G M, ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS,...

Hoeffding's Lemma gives an integral representation of the covariance of two random variables in terms of difference between their joint and marginal probability functions. This identity has been found to be useful tool in studying the dependence structure of various random vectors. A generalization of this result for more than 2 random variables is given. This involves an integral representation of the multivariate joint cumulant. Applications of this result include characterizations of...

Topics: DTIC Archive, Block,Henry W, PITTSBURGH UNIV PA DEPT OF MATHEMATICS AND STATISTICS, *MULTIVARIATE...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all...

Topics: DTIC Archive, Gupta,Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *ANALYSIS OF VARIANCE,...

Most of the world's computer centers use congruential random number generators. This note points out that such random number generators produce points in 2,3,4,... dimensions which are too regular for many Monte Carlo calculations. The trouble is that the points fall exactly on a lattice with quite a gross structure. The paper gives details of the degree of regularity of such generators in terms of sets of relatively few parallel hyperplanes which contain all of the points produced by the...

Topics: DTIC Archive, Marsaglia, George, BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH...

We say that the random variable X is more variable than Y if E(f(X)) greater than or equal to E(f(Y)) for all increasing convex functions f. We prove a preservation, under random sized sums, property of this ordering and then apply it to branching processes and shock models.

Topics: DTIC Archive, Ross,Sheldon M, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *STOCHASTIC...

We say that the random variable X is more variable than Y if E(f(X)) greater than or equal to E(f(Y)) for all increasing convex functions f. We prove a preservation, under random sized sums, property of this ordering and then apply it to branching processes and shock models.

Topics: DTIC Archive, Ross,Sheldon M, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *STOCHASTIC...

We say that the random variable X is more variable than Y if E(f(X)) greater than or equal to E(f(Y)) for all increasing convex functions f. We prove a preservation, under random sized sums, property of this ordering and then apply it to branching processes and shock models.

Topics: DTIC Archive, Ross,Sheldon M, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *STOCHASTIC...