bluuebunny/crossref_metadata_2025 huggingface dataset:
Data Shuffling—A New Masking Approach for Numerical Data
Authors: Muralidhar Krishnamurty , Sarathy Rathindra
Published: April 2006

This study discusses a new procedure for masking confidential numerical data—a procedure called data shuffling—in which the values of the confidential variables are “shuffled” among observations. The shuffled data provides a high level of data utility and minimizes the risk of disclosure. From a practical perspective, data shuffling overcomes reservations about using perturbed or modified confidential data because it retains all the desirable properties of perturbation methods and performs better than other masking techniques in both data utility and disclosure risk. In addition, data shuffling can be implemented using only rank-order data, and thus provides a nonparametric method for masking. We illustrate the applicability of data shuffling for small and large data sets.
Teach phenomenology the bomb: Starship Troopers, the technologized body, and humanitarian warfare
Authors: Leonard Philip
Published: April 2006

Paul Verhoeven's SF films are often concerned with how the future body will be reshaped as a technological device. Starship Troopers strangely departs from Verhoeven's own work, other SF films, and current directions in cultural theory by seeing the future body as one that is
more organic than mechanical. Drawing upon and challenging ideas developed by Paul Virilio, this article argues that Starship Troopers' departure from the notion of the post-human mechanized body needs to be understood not as a nostalgic reassertion of de-technologized subjectivity.
Rather, Verhoeven's film sees the idea of the pure body as a dangerous anachronism. And, this article further argues, Starship Troopers suggests that narratives of human salvation - such as those that arose during Nato's interventions in the Balkans - often conceal an appetite for territorial
conquest.
Reviews
Authors: Kusnr Jaroslav
Published: April 2006

Wallace Stevens and the Limits of Reading and Writing, Bart Eeckhout (2002) Columbia and London: University of Missouri Press, 303 pp., 33.50
Branching processes with terminal types: application to context-free grammars
Authors: Sankoff David
Published: April 2006

In this note we consider multi-type branching processes where certain terminal types of particles, once created, are subject neither to death nor to further reproduction.
On certain unrestricted, linear, unit step, continuous time random walks
Authors: Gibson A. E. , Conolly B. W.
Published: April 2006

A basic process of simple queueing theory is S(t), an integer valued stochastic process which represents the “number of clients present, including the one in service” at epoch t. The queueing context physically limits S(t) to non-negative values, but if this impenetrable barrier is removed thereby permitting S(t) to assume negative values as well, we have a “randomized random walk” in which S(t) represents the position at time t of a mythical particle which moves on the x-axis according to the rules of the walk. The nomenclature “randomized random walk” is due to Feller (1966a). S(t) changes by unit positive or negative amounts, and our basic assumption is that the time intervals τ/σ separating successive positive/negative steps are i.i.d. with continuous d.f.'s. A(t)/B(t) (A(0)/B(0) = 0) possessing p.d.f.'s. a(t)/b(t): τ and σ are further assumed to be statistically independent. When A(t) = 1 – e–λt and B(t) = 1 – e–μt, we have a generalization of the M/M/1 queueing process which we shall denote by M/M. The walk generated by A(t) = 1 – e–λt and B(t) arbitrary may similarly be denoted by M/G. For G/M we clearly mean A(t) arbitrary and B(t) = 1 – e–μt. M/M has received extensive treatment elsewhere (cf. Feller (1966a), (1966b); Takács (1967); Gibson (1968); Conolly (1971)), and will not be considered here. Our interest centers on certain aspects of M/G and G/M, but since each is the dual of the other (loosely, G/M is M/G “upside down”) it is sufficient to restrict attention to one of them, as convenient; pointing out, where necessary, the interpretation in terms of the other.
On sums of random variables defined on a two-state Markov chain
Authors: Helgert H. J.
Published: April 2006

Assume the sequence of random variables x0, x1, x2, ··· forms a two-state, homogeneous Markov chain with transition probabilities

and initial probabilities
Convergence to equilibrium of the two locus additive viability model
Authors: Karlin Samuel , Feldman Marcus W.
Published: April 2006

Consider a deterministic diploid population and a character determined by two loci with allelesA, aat the first andB, bat the second. When the effects of the alleles at each of the two loci on the relative fitnesses of the genotypes are additive, the selection matrix may be written
A note on the queueing system Ek/G/1
Authors: Henderson J. , Finch P. D.
Published: April 2006

In this note we present results for the queueing system Ek/G/1 which are analogous to those obtained in Finch (1969) for the queueing system GI/Ek/1. As in that paper we adopt the notation and terminology of Kingman (1966) without further comment.
A note on stochastic processes with independent increments taking values in an abelian group
Authors: Bingham M.S.
Published: April 2006

It is well known that any stochastically continuous real valued stochastic process with independent increments defined on a compact time interval can be decomposed into a sum of independent processes, one of which is Gaussian with continuous sample paths, and the remainder of which have sample paths which are continuous except at a finite number of points with the discontinuities occurring at Poisson time points. The purpose of this note is to announce a proof of the above theorem in the case where the process takes values in an abelian group G. The detailed proof will appear elsewhere. The basic ideas of the proof in the case when G is finite dimensional Euclidean space are contained in Chapter VI of Gikhman and Skorohod (1965).
Single server queue with uniformly bounded virtual waiting time
Authors: Cohen J. W.
Published: April 2006

In a previous paper [4] the author studied the stochastic process {wn, n = 1,2, …}, recursively defined by

with K a positive constant, τ1, τ2, … σ1, σ2, …, independent, nonnegative stochastic variables. τ1,τ2…, are identically distributed, and σ1,σ2,…, are also identically distributed variables. For this process the generating function of the Laplace-Stieltjes transforms of the joint distribution of Wn, σ2 + … + σn and τ1 + … + τn−1 has been obtained. Closely related to the process {wn, n = 1, 2,…} is the process {un, n = 1, 2,…} with {un = K + [wn + τn − K]−, n = 1,2,…; these are dual processes.

In the present paper we study the stationary distributions of the processes {wn, n= 1,2, …} and {un, n = 1,2, …}, and the distributions ot the entrance times and return times of the events “wn, n = 0” and “un = K” for some n, for discrete as well as for continuous time. For these events various taboo probabilities are also investigated. The mathematical descri ption of the processes {wn, n = 1,2, …} and {un, n= 1,2, …} gives all the necessary information about the time-dependent behaviour for the general dam model with finite capacity K, since the process {wn, n= 1,2, …} is the basic process for such dam models. In Sections 5, 6 and 7 the general theory is applied to the models M/G/1 and G/M/1. Complete explicit solutions are obtained for these models.

The present theory also leads to new and important results for the queueing system or dam model G/G/1 with infinite capacity. For instance the joint distribution of the busy period (or wet period) and of the supremum of the dam content dunng this period is obtained.
Transient behavior of multi-server queues with recurrent input and exponential service times
Authors: Bhat U. Narayan
Published: April 2006

Customers arrive in a recurrent process and get served by one of the s (≧1) servers wit han exponential service time distribution. The equilibrium behavior of the queue length process has been studied by earlier authors. In this paper the transient behavior of this process is investigated.
On probability properties of measures of random sets and the asymptotic behavior of empirical distribution functions
Authors: Ailam Gedalia
Published: April 2006

Probability properties of the measure of the union of random sets have theoretical as well as practical importance (David (1950), Garwood (1947), Hemmer (1959)). In the present paper we derive asymptotic properties of the distributions of these measures and apply the derived properties to the investigation of the asymptotic behavior of empirical distribution functions. Thus, an asymptotic distribution function for the relative lengths of steps in the empirical distribution function is obtained.
Some new results in the mathematical theory of phage-reproduction
Authors: Puri Prem S.
Published: April 2006

In the theory of phage reproduction, the mathematical models considered thus far (see Gani [5]) assume that the bacterial burst occurs a fixed time after infection, after a fixed number of generations of phage multiplication, or when the number of mature bacteriophages has reached a fixed threshold. In the present paper, a more realistic assumption is considered: given that until timetthe bacterial burst has not taken place, its occurence betweentandt+ Δtis a random event with probabilityf(· |t)Δt+o(Δt), wherefis a non-negative and non-decreasing function of the numberX(t) of vegetative phages and ofZ(t), the number of mature bacteriophages at timet.More specifically it is assumed thatf=b(t)X(t) +c(t)Z(t) withb(t),c(t) ≦ 0. HereX(t) denotes the survivors in a linear birth and death process andZ(t) the number of deaths until timet.The joint distribution ofXTandZT, the respective numbers of vegetative and mature bacteriophages at the burst time is considered. The distribution ofZTis then fitted to some observed data of Delbrück [2].
On the fluctuations of election returns
Authors: Takács Lajos
Published: April 2006

Suppose that in a ballot candidate A scores a votes and candidate B scores b votes and all the possible voting records are equally probable. Denote by αr and βr the number of votes registered for A and B respectively among the first r votes counted. For j= 0, 1,···, a + b define Pj(a, b) as the probability that the inequality αr > aβr/b holds for exactly j subscripts r = 1, 2, .., a + b.
A note on linear estimation of the intensity in a doubly stochastic Poisson field
Authors: Grandell Jan
Published: April 2006

A realization of a doubly stochastic Poisson field is assumed to be observed in a Borel set S ⊂ Rk. The best linear estimate of the realization of the intensity field (at an arbitrary but fixed point x ∈ S) which generated the observation is obtained.
Goofspiel — the game of pure strategy
Authors: Ross Sheldon M.
Published: April 2006

The game of pure strategy, sometimes called Goofspiel or Gops (see [2] and [3]), is played by two players, using a normal deck of cards, as follows. The 13 clubs are first taken out of the deck and of the remaining 39 cards the 13 hearts are given to Player I, the 13 diamonds to Player II, and the 13 spades are placed face down in the center. The spades are shuffled and one is turned face up. At this point, the two players choose one of their cards and then simultaneously discard it. The one who discards the higher card (ace being low, king high) wins from the other an amount equal to the value of the upturned spade (ace = 1, king = 13). If both players discard the same card, then neither wins. The three cards are then thrown away, a new spade upturned and the game continues. After 13 plays, there are no remaining cards and the game ends.
Some renewal process models for single neuron discharge
Authors: Hochman Howard G. , Fienberg Stephen E.
Published: April 2006

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.
Times to intermittent and to permanent failures as Brownian crossing times
Authors: Nádas Arthur
Published: April 2006

Consider a device which begins operating at time t = 0 and then operates continuously in time. The operation of the device is satisfactory so long as a physical parameter X(t) of the device remains less than a critical value c > 0 (X(0) = 0). The device does not operate satisfactorily (i.e., it is “failed”) at a time t if X(t) ≧ c. Suppose that X(t) is a random variable with mean EX(t) = ta (a> 0), i.e., the device parameter X drifts with a linear rate a.
A one dimensional random space-filling problem
Authors: Mullooly John P.
Published: April 2006

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx, the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.
A Note on Absorption Probabilities for a Random Walk Between a Reflecting and an Absorbing Barrier
Authors: Hardin J.C. , Sweet A.L.
Published: April 2006

Generating functions for the absorption probabilities for a random walk on the integers {0,1, …, b}, where 0 is an absorbing barrier and b a semi-reflecting barrier have been obtained by Weesakul [1] and Neuts [2]. However, determination of explicit expressions for the absorption probabilities from the generating functions is generally quite difficult. In this note, two cases where this is possible are presented.
A renewal density theorem in the multi-dimensional case
Authors: Mode Charles J.
Published: April 2006

In this note a renewal density theorem in the multi-dimensional case is formulated and proved. Let f(x) be the density function of a p-dimensional random variable with positive mean vector μ and positive-definite covariance matrix Σ, let hn(x) be the n-fold convolution of f(x) with itself, and set

Then for arbitrary choice of integers k1, …, kp–1 distinct or not in the set (1, 2, …, p), it is shown that under certain conditions

as all elements in the vector x = (x1, …, xp) become large. In the above expression μ‵ is interpreted as a row vector and μ a column vector. An application to the theory of a class of age-dependent branching processes is also presented.
The transition probabilities of the extended simple stochastic epidemic model and the Haskey model
Authors: Kryscio Richard J.
Published: April 2006

We present a solution to a special system of Kolmogorov forward equations. We use this result to present a useful expression for the transition probabilities of the extended simple stochastic epidemic model and an epidemic model involving cross-infection between two otherwise isolated groups.
Taboo extinction, sojourn times, and asymptotic growth for the Markovian birth and death process
Authors: Waugh W. A. O'n.
Published: April 2006

A well-known result in the theory of branching processes provides an asymptotic expression for the population size (valid for large times) in terms of a single random variable, multiplied by a deterministic exponential growth factor. In the present paper this is generalized to a class of size-dependent population models. The work is based on the series of sojourn times. An essential tool is the use of probabilities conditional upon non-extinction (taboo probabilities).
On the estimation of intensities in a stochastic process generated by a stochastic intensity sequence
Authors: Grandell Jan
Published: April 2006

A stationary doubly stochastic Poisson sequence is considered. Asymptotic properties of the best linear estimates of the intensities are investigated.
An inequality for a metric in a random collision process
Authors: Nishimura Shōichi
Published: April 2006

A random collision process with transition probabilities belonging to the same type of distribution is considered. It was proved that if the characteristic function of the initial distribution has a positive radius of convergence, then the sequence {Fn(x)} converges weakly to a distribution G(x) [9]. We define a metric e1[Fn;G], which is analogous to the functional e[f] introduced by Tanaka to Kac's model of Maxwellian gas [10]. We prove that e1[Fn; G] is monotone non-increasing as n → ∞, and also the convergence of the sequence {Fn(x)} under the weaker assumption that for some a > 1 the initial distribution has an ath moment.
Information density phenomena and random packing
Authors: Dolby James L. , Solomon Herbert
Published: April 2006

A density model for various phenomena with densities much smaller than those explored by the Zipf model is developed. The density of spherical random packing in n dimensions serves as a model for relative frequency of length of monosyllabic words in English and also for the relative frequency of degree holders in the U.S. at various levels of educational attainment.
The distribution of the maximum of a random number of random variables with applications
Authors: Galambos Janos
Published: April 2006

The asymptotic distribution of the maximum of a random number of random variables taken from the model below is shown to be the same as when their number is a fixed integer. Applications are indicated to determine the service time of a system of a large number of components, when the number of components to be serviced is not known in advance. A much slighter assumption is made than the stochastic independence of the periods of time needed for servicing the different components. In our model we assume that the random variables can be grouped into a number of subcollections with the following properties: (i) the random variables taken from different groups are asymptotically independent, (ii) the largest number of elements in a subgroup is of smaller order than the overall number of random variables. In addition, a very mild assumption is made for the joint distribution of elements from the same group.
La formule de crofton pour les sections Épaisses
Authors: Matheron Georges
Published: April 2006

The classical Crofton formula is generalized to the case of thick sections, and the corresponding corrective formulae are given.
Some asymptotic results for optimal stopping based on capture times
Authors: Wardrop Robert L.
Published: April 2006

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Zi; where Z1, Z2, …, Zn are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.
Estimation of the mean and the initial probabilities of a branching process
Authors: Dion Jean-Pierre
Published: April 2006

In this article, we consider maximum likelihood estimators of the initial probabilities and the mean of a supercritical Galton-Watson process; we find for these estimators, as well as for the Lotka-Nagaev estimator of the mean, the asymptotic distributions and deduce confidence intervals. As these results hold even if the independence between individuals of the same generation is not satisfied, application to living populations may be considered.
Recursive matrix games
Authors: Orkin Michael
Published: April 2006

“Recursive” games were first defined and studied by Everett. Related results can be found in Gillette, Milnor and Shapley, and Blackwell and Ferguson. In this paper we introduce the notion of a recursive matrix game, which we believe eliminates the vagueness but none of the useful generality of the earlier definition. We then give an inductive proof (different from the proof in [3]) that these games have a value, with ∊-optimal stationary strategies available to each player. We also apply the result and show how a class of games studied in a different framework are games of this type and thus have a value.
Complements to heavy traffic limit theorems for the GI/G/1 queue
Authors: Whitt Ward
Published: April 2006

A bound on the rate of convergence and sufficient conditions for the convergence of moments are obtained for the sequence of waiting times in the GI/G/1 queue when the traffic intensity is at the critical value ρ = 1.
Study of a network of serial and non-serial servers with phase type service and finite queueing space
Authors: Arya Krishan Lall
Published: April 2006

The paper develops the steady-state solution of a finite space queueing system wherein each of the two non-serial servers is separately in series with two non-serial servers. It is assumed that the arriving units of the same type may demand a different number of service phases. Poisson arrivals and exponential service times are assumed at all the four channels of the system. Service of units is completed on a first-come, first-served basis at each channel. The steady-state solution for infinite queueing space is obtained as a special case of finite queueing space.
A note on a singular diffusion equation in population genetics
Authors: Aase Knut
Published: April 2006

This note points out an error made in an earlier paper treating a diffusion equation for the probability distribution of gene frequencies under selection. The main interest lies in the orthogonality properties of certain eigenfunctions and the determination of the corresponding Fourier coefficients. Two particular cases of selection parameter values are considered. Approximate formulas are given for the two smallest eigenvalues for arbitrary values of the selection parameters.
Partial attraction of maxima
Authors: Green Richard F.
Published: April 2006

There exist three classes of probability laws that are stable for maxima. A number of well-known distributions lie in the domains of attraction of these laws. This fact is sometimes exploited by fitting the distribution of maxima with one of the stable laws. Such a procedure may well be misguided, however, since distributions exist which produce maxima having any desired distribution and not just a stable type. In this paper partial attraction of maxima is defined and it is shown that all distributions have a non-empty domain of partial attraction of maxima. In fact, there exists a distribution that lies simultaneously in the domain of partial attraction of maxima of all distributions.
On the distribution of hits
Authors: Rudolfer S. M.
Published: April 2006

A marksman fires at a target which consists of s zones. At each stage, he shoots independently of his previous efforts and has a probability p0 of missing the target which is a function of the probabilities p1…, ps of hitting zones 1, …, s, respectively. The distribution of the number of hits Xn on the target after n shots is obtained and used to study the marksman's optimal strategy for the case and α0 ≦ 1.
A limit theorem for semi-Markov processes
Authors: Szász Domokos
Published: April 2006

A limit theorem is proved for semi-Markov processes, which depend on a small parameter, tending to 0, in the case when the processes have an absorbing state and some asymptotically non-essential states and one asymptotically essential state. The application of the theorem is illustrated by an example from reliability theory.
Bounds for coverage probabilities with applications to sequential coverage problems
Authors: Cooke Peter J.
Published: April 2006

This paper discusses general bounds for coverage probabilities and moments of stopping rules for sequential coverage problems in geometrical probability. An approach to the study of the asymptotic behaviour of these moments is also presented.
Ergodic properties of a two-dimensional binary process
Authors: Galbraith R. F. , Walley D.
Published: April 2006

Sufficient conditions are derived for ergodicity of the two-dimensional process of binary variables discussed by Galbraith and Walley (1976).
On a stopping time of Starr and its use in estimating the number of transmission sources
Authors: Vardi Yehuda
Published: April 2006

Consider N sources, each of which transmits signals according to a renewal process with a common, known, underlying distribution. Sequential point estimators for N, which are asymptotically efficient in comparison to the best fixed stopping strategy, are derived. Confidence statements for N, and applications to the problem of estimating finite populations are discussed.

The exact limiting distribution, and moments, of the stopping time we use, which was suggested by Starr, are derived.
Gaussian approximation of some closed stochastic epidemic models
Authors: Wang Frank J. S.
Published: April 2006

A generalization of Bailey's general epidemic model is considered. In this generalized model, it is assumed that the probability of any particular susceptible becoming infected during the small time interval (t, t + Δt) is α(X(t))Δt + o(Δt), for some function a, where X(t) is the proportion of infected individuals in the entire population, the probability that an infected individual is infected for at least a length of time t is F(t), and recovered individuals are permanently immune from further attack. In this paper, central limit theorems are obtained for the proportion of infected individuals and the proportion of susceptibles in the entire population.
Estimators for distances
Authors: Gilbert E. N.
Published: April 2006

This paper compares estimators of u = |P2 — P1| based on partial knowledge about points P1, P2 which are chosen independently from the same probability distribution in the plane. Typical estimators are the conditional expectations E(u | r1, r2), E(u | s), E(u | rM), E(u | θ) where ri is the distance from Pi to the origin 0, s = r1 + r2, rM = Max{r1, r2}, θ = ∠ P10P2. These expectations are the least squares estimators, given the conditioned variables. Simpler linear estimators are also considered.
On the convergence of the supercritical branching processes with immigration
Authors: Cohn Harry
Published: April 2006

It is shown for a supercritical branching process with immigration that if the log moment of the immigration distribution is infinite, then no sequence of positive constants {cn} exists such that {Xn/cn} converges in law to a proper limit distribution function F, except for the case F(0 +) = 1. Seneta's result [1] combined with the above-mentioned one imply that if 1 < m < ∞ then the finiteness of the log moment of the immigration distribution is a necessary and sufficient condition for the existence of some constants {cn} such that {Xn/cn} converges in law to a proper limit distribution function F, with F(0 +) < 1.
On a simple formula for random mappings and its applications
Authors: Burtin Y. D.
Published: April 2006

A random mapping of a countable set N into itself is studied. An explicit formula is found for the probability that a subset of N will not contain cycles of the mapping. This formula is applied then for a detailed asymptotic analysis of two special mappings.
Functional normalizations for the branching process with infinite mean
Authors: Barbour Andrew D. , Schuh H.-J.
Published: April 2006

It is well known that, in a Bienaymé-Galton–Watson process (Zn) with 1 < m = EZ1 < ∞ and EZ1 log Z1 <∞, the sequence of random variables Znm –n converges a.s. to a non–degenerate limit. When m =∞, an analogous result holds: for any 0< α < 1, it is possible to find functions U such that α n U (Zn) converges a.s. to a non-degenerate limit. In this paper, some sufficient conditions, expressed in terms of the probability generating function of Z1 and of its distribution function, are given under which a particular pair (α, U) is appropriate for (Zn). The most stringent set of conditions reduces, when U (x) x, to the requirements EZ1 = 1/α, EZ1 log Z1 <∞.
On some percolation results of J. M. Hammersley
Authors: Oxley J. G. , Welsh D. J. A.
Published: April 2006

We examine how much classical percolation theory on lattices can be extended to arbitrary graphs or even clutters of subsets of a finite set. In the process we get new short proofs of some theorems of J. M. Hammersley. The FKG inequality is used to get an upper bound for the percolation probability and we also derive a lower bound. In each case we characterise when these bounds are attained.
Extended block replacement policy with used items
Authors: Tango Toshiro
Published: April 2006

Block replacement policy, under which items are replaced at constant intervals of time and at failure, is wasteful because sometimes almost new items are also replaced. In order to eliminate this kind of waste, the following replacement policy is suggested.

(1) Items are exchanged for new items at time kT (k ··· 1, 2, …).

(2) If items fail in [(k – 1) T, kT – v), they are replaced by new items, and if in [kT – v, kT), they are replaced by used items.

The results of this ‘extended block replacement policy with used items' are studied for the Erlang lifetime distribution.
Limit theorems for general size distributions
Authors: Chen Wen-Chen
Published: April 2006

Let X1, X2, · ··, Xn, · ·· be independent and identically distributed non-negative integer-valued random variables with finite mean and variance. For any positive integer n and m we consider the random vector i.e., L has the same distribution as the conditional distribution of (X1, · ··, Xm) given the condition It is easy to see that our model includes the classical urn model, the Bose–Einstein urn model and the Pólya urn model as special cases. For any non-negative integer s define G(s) = the number of Li′s such that Li = s, and U = the number of Li′s such that Li is an even number; in this paper we study the asymptotic behaviour of the random variables considered above. Some central limit theorems and a multinormal local limit theorem are proved.
On the convergence of stochastically monotone sequences of random variables and some applications
Authors: Cohn Harry
Published: April 2006

The paper is concerned with the relationship between various modes of convergence for stochastically monotone sequences of random variables. A necessary and sufficient condition, as well as a sufficient condition, for convergence in probability of a vaguely convergent sequence are given. If, in addition, the sequence is assumed Markovian the same conditions are shown to pertain to almost sure convergence. A counterexample in the case when stochastic monotonicity fails is presented and some applications to branching processes are discussed.
On the autocorrelation structure for seasonal moving average models and its implications for the Cramér-Wold factorization
Authors: Godolphin E. J.
Published: April 2006

An account is given of the autocorrelation theory of seasonal moving average models, using a vector representation defined by the author. It is shown that the autocorrelation structure of a seasonal moving average is reducible to that of a certain non-seasonal moving average, independently of the value of the seasonal periodicity if sufficiently large. It is pointed out that existing methods for the Cramér–Wold factorization discussed in Godolphin (1976) can easily be adapted to contend with the seasonal case.
An upper bound for multi-channel queues
Authors: Wolff Ronald W.
Published: April 2006

Moments of the delay distribution and other measures of performance for a multi-channel queue are shown to be bounded above by corresponding quantities for one or a collection of single-channel queues.
Some more results for the stable M/G/1 queue in heavy traffic
Authors: Ott Teunis J.
Published: April 2006

In a previous paper the author derived some results describing the tail-behavior of the busy time distribution function B of a stable M/G/1 queue in heavy traffic, i.e., some results were given for B (t), t large. In this paper some complementary results are given, in the same heavy-traffic situation, for B (t), t small.
A uniform limit theorem and exponential limit law for critical multitype age-dependent branching processes
Authors: Goldstein Martin I.
Published: April 2006

Let Z(t) ··· (Z1(t), …, Zk (t)) be an indecomposable critical k-type age-dependent branching process with generating function F(s, t). Denote the right and left eigenvalues of the mean matrix M by u and v respectively and suppose μ is the vector of mean lifetimes, i.e. Mu = u, vM = v.

It is shown that, under second moment assumptions,

uniformly for s ∈ ([0, 1]k of the form s = 1 – cu, c a constant. Here vμ is the componentwise product of the vectors and Q[u] is a constant.

This result is then used to give a new proof of the exponential limit law.
Asymptotic properties of discrete duels
Authors: Kimeldorf George , Lang John Patrick
Published: April 2006

For fixed accuracy functions, let Gnm be a discrete-fire (silent, noisy, or silent-noisy) duel in which the amounts of ammunition available to the two players are n and m, respectively. As n and m both become large, a class of ‘ε -optimal' pure strategies (with support (anm, 1)) is derived. If vnm denotes the value of Gnm, the asymptotic relationships among the quantities n, m, vnm, and anm are investigated.
On the output theorem of queueing theory, via filtering
Authors: Brémaud P.
Published: April 2006

We prove and extend Burke's output theorem for queues in equilibrium with the help of a filtering formula giving the time evolution of the least square estimate of the state with respect to the output.
The probability that two samples in the plane will have disjoint convex hulls
Authors: Rogers L. C. G.
Published: April 2006

Suppose given an absolutely continuous distribution on the plane, and points Pi, · · ·, Pj, Πt, · · ·, Πk chosen independently according to the given distribution. Denoting by Gj the convex hull of {Pi, · · ·, Pj}, and by Γk the convex hull of (Πt, · · ·, Πk}, and writing pjk for the probability that Gj and Γk are disjoint, certain properties of the array {pjk; j, k = 1,2, · · ·} are established, including a recurrence generating the array in terms of {p1n; n = 1,2, · · ·}, and asymptotic results for {pnn; n = 1,2, · · ·}. Some examples are considered.
Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities
Authors: Mertens Jean-François , Samuel-Cahn Ester , Zamir Shmuel
Published: April 2006

For an aperiodic, irreducible Markov chain with the non-negative integers as state space it is shown that the existence of a solution to in which yi → ∞is necessary and sufficient for recurrence, and the existence of a bounded solution to the same inequalities, with yk < yo, · · ·, yN–1 for some k ≧ N, is necessary and sufficient for transience.
On the past history of an allele now known to have frequencyp
Authors: Sawyer Stanley
Published: April 2006

Consider a diploid population ofNindividuals undergoing random mating and mutation as in the infinite-allele Wright model. Choose a particular gene in generationQfor largeQ, and letft(0 ≦t≦Q) be the frequency of the allelic type of the predecessor of that particular gene (or the gene itself) in generationt. By considering a ‘diffusion approximation' {xt} of {ft}, we find the distribution of the age of an allelic type now known to have frequencyp, and of its distribution of frequencies since the allele came into existence. A novelty here is that the process {xt} is not a diffusion, but a process with jumps; it hasx =0 as an inaccessible entrance boundary but periodically jumps to it from the interior of [0, 1]. The formulas obtained are the same as those derived by Maruyama and Kimura, who used a totally different approach.
Finding the edge of a Poisson forest
Authors: Ripley B. D. , Rasson J.-P.
Published: April 2006

The points of a homogeneous Poisson process within a compact convex set are observed. We consider how to reconstruct this domain from the observations.
Velocities of propagation for stepping-stone models of population growth
Authors: Renshaw Eric
Published: April 2006

A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours only. Exact expressions are derived for both the asymptotic velocity of propagation and the shape of the wave profile as the population spreads along the axis, and it is shown that they are identical with the saddle point approximations developed by Daniels.
On the length distribution of stochastic subarcs of a rectifiable arc
Authors: Mann J. E.
Published: April 2006

Suppose that A1, A2, · ··, An are disjoint subarcs of a rectifiable arc A ⊆ Rk. The location and length of each subarc are assumed to be continuous random variables. An expression for the expected fraction of A covered by subarcs each of length greater than τ ≧ 0 is obtained and applied to two conceptually distinct problems associated with light penetration of an absorbing medium.
Optimal estimation of the criticality parameter of a supercritical branching process having random environments
Authors: Pakes Anthony G. , Heyde C. C.
Published: April 2006

Let {Zn} be a Galton-Watson process with i.i.d. random environments. This paper is concerned with estimation of π= E log Mn, where Mn is the. conditional expected number of offspring per nth generation individual, given the environments, when this quantity is positive. We show that, given non-extinction, {n-1 log Zn} is asymptotically the most efficient estimator of πamongst a broad class of those that are linear combinations of {log Zi: 1 ≦ j ≦ n}·
Isolated nearest neighbors
Authors: Pickard David K.
Published: April 2006

For point processes, a pair of points is isolated if each is the nearest neighbor of the other, and its degree of isolation is the relative distance to the next-nearest point. The frequency with which such pairs occur and the distribution of their degree of isolation are obtained for Poisson processes in ℝv. Similar results are obtained for some related models, incidentally solving a problem proposed by D. P. Shine.
Random coverage of a circle with applications to a shadowing problem
Authors: Yadin M. , Zacks S.
Published: April 2006

The coverage problem on the circle is considered from the shadowing process point of view. A random number of shadow arcs are distributed on a circle. The length of each arc is a random variable which depends on the random diameter of a shadowing disk and its random location. Formulae are derived for the numerical determination of the moments of the measure of vacancy of arcs on the circle, for a special example. An approximation to the distribution of the measure of vacancy is also provided.
A connection between the limit and the maximum random variable of a branching process in varying environments
Authors: Klebaner F. C. , Schuh H.-J.
Published: April 2006

We show for a certain class of Galton–Watson branching processes in varying environments (Zn)n that moments of the maximum random variable supnZn/Cn exist if and only if the same moments of limnZn/Cn exist, where Cn is a sequence of suitable constants.
The effect of differential reproductive rates on the survival of a gene represented in a founder population
Authors: Heyde C. C.
Published: April 2006

Gene survival in a population which increases without density dependence is considered using a generalization of the Moran model for haploid individuals in which we have differential reproductive rates. It is shown under very mild conditions that ultimate fixation is certain. This provides some mathematical support for the phenomenon of reduced genetic variability in isolated populations established from founder groups.
Bounds for the probability of complete intersection of random chords in a circle
Authors: Gates John
Published: April 2006

Upper and lower bounds are obtained for the integral giving the probability that n invariant chords to a circle all intersect each other.
A multivariate IFR class
Authors: Savits Thomas H.
Published: April 2006

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.
A note on strong unimodality and dispersivity
Authors: Droste W. , Wefelmeyer W.
Published: April 2006

A distribution R is ‘more dispersed' than a distribution P if any two quantiles of R are more widely separated than the corresponding quantiles of P. Lewis and Thompson (1981) prove that a non-degenerate distribution P is strongly unimodal if and only if it is ‘dispersive', i.e. if P∗ Q1 is more dispersed than P∗ Q2 whenever Q1 is more dispersed than Q2. For P admitting a positive Lebesgue density, we prove that P is strongly unimodal if and only if P ∗ Q is more dispersed than P for every distribution Q. Hence the latter property also characterizes the dispersivity of P.
Estimation and optimal stopping in a debugging model with masking
Authors: Siegrist Kyle
Published: April 2006

A system has an irremovable failure source and a number of removable flaws. The system undergoes a sequence of trials designed to detect and remove the flaws. On each trial, the irremovable failure source may cause failure which in turn may block the detection of any flaws. If not, then each flaw in the system, independently, is detected on that trial with a certain probability and each detected flaw, independently, is removed from the system with a certain probability before the next trial. Distributions of the outcomes of the trials are obtained. Point estimates of the parameters, based on accumulated trial data, are given. Assuming that certain costs are associated with trials, optimal stopping rules and a cost-benefit analysis are given.
Weak convergence of the adjusted range of cumulative sums of exchangeable random variables
Authors: Troutman Brent M.
Published: April 2006

Let be the adjusted range of the cumulative sums of a sequence , where . Weak convergence results for random functions constructed from cumulative sums of {Xs} are used to obtain the asymptotic distribution and moments of when {Xs} are exchangeable, or symmetrically dependent, random variables.
The rumour process
Authors: Dunstan Ross
Published: April 2006

The general stochastic epidemic model is used as a model for the spread of rumours. Recursive expressions are found for the mean of the final size of each generation of hearers. Simple expressions are found for the generation size and the asymptotic form of its final size in the deterministic model. An approximating process is presented.
Recognition of triangles and quadrilaterals by chord length distribution
Authors: Gates J.
Published: April 2006

It is shown how a triangle can be recognised from the odd moments of the length of random chords and how a quadrilateral can be recognised from the derivative of its chord length density.
Connectivity of random graphs
Authors: Dorea Chang C. Y.
Published: April 2006

We consider a random field {Xij, i, j = 1, ···, n} where the random variables Xij takes on values 1 or 0. The collection {Xij} can be viewed as a random graph with nodes {1, ···, n} by interpreting Xij = 1 as the existence of an arc emanating from the node i to the node j. Such a representation will enable us to study ordered and unordered graphs, being also the general representation of a random graph. In this note the probability that the graph is connected is computed under the condition that ΣiXki=l for k = 1, · ··, n. This result extends Ross's recent theorems on connectivity of random graphs.
Optimal stopping in a partially observable binary-valued markov chain with costly perfect information
Authors: Monahan George E.
Published: April 2006

The problem of optimal stopping in a Markov chain when there is imperfect state information is formulated as a partially observable Markov decision process. Properties of the optimal value function are developed. It is shown that under mild conditions the optimal policy is well structured. An efficient algorithm, which uses the structural information in the computation of the optimal policy, is presented.
On the mean number of random digits until a given sequence occurs
Authors: Blom Gunnar
Published: April 2006

Random digits are collected one at a time until a given sequence is obtained. The mean number of digits until this happens is determined. Generalizations are given to a stopping region consisting of several sequences of equal length.
The visibility of stationary and moving targets in the plane subject to a Poisson field of shadowing elements
Authors: Yadin M. , Zacks S.
Published: April 2006

A methodology for an analytical derivation of visibility probabilities of n stationary target points in the plane is developed for the case when shadows are cast by a Poisson random field of obscuring elements. In addition, formulae for the moments of a measure of the total proportional visibility along a star-shaped curve are given.
Comparison of two replacement policies
Authors: Lešanovský Antonín
Published: April 2006

Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.
On Wiener–Ito representation and the best linear predictors for bilinear time series
Authors: Terdik Gy. , Rao T. Subba
Published: April 2006

This paper gives the necessary and sufficient condition for the second-order stationarity of lower triangular bilinear models; this condition is in terms of norms of higher-order transfer functions. The spectral density function of the process is evaluated in terms of the transfer functions, and it is shown that the second-order structure is similar to a linear ARMA model with uncorrelated errors. The best linear predictor is obtained and it is shown that the variance of the prediction error is always greater than the optimal prediction error variance obtained from the bilinear model. An expression for the bispectral density function is also obtained.
A Markov chain approach to periodic queues
Authors: Asmussen Søren , Thorisson Hermann
Published: April 2006

We consider GI/G/1 queues in an environment which is periodic in the sense that the service time of the nth customer and the next interarrival time depend on the phase θ n at the arrival instant. Assuming Harris ergodicity of {θ n} and a suitable condition on the traffic intensity, various Markov chains related to the queue are then again Harris ergodic and provide limit results for the standard customer- and time-dependent processes such as waiting times and queue lengths. As part of the analysis, a result of Nummelin (1979) concerning Lindley processes on a Markov chain is reconsidered.