bluuebunny/crossref_metadata_2025 huggingface dataset:
The statistical analysis of direct repeats in nucleic acid sequences
Authors: Shukla Rakesh , Srivastava R. C.
Published: April 2006

Sequence symmetries in DNA and RNA are being discovered at an increasing rate. Conjectures and hypotheses are being proposed for their possible structural and functional role in the nucleic acid. In this paper a probability model is studied which evaluates the probabilities of various repeats occurring by chance alone. Expressions are derived for the mean and variance of the statistics employed. The central limit theorem for dependent trials is used to obtain the asymptotic distributions. An indication is given of how to use the model to search for various gene amplification events in the evolutionary history of the sequences.
A note on first-passage time and some related problems
Authors: Nobile A. G. , Ricciardi L. M. , Sacerdote L.
Published: April 2006

Expansions for the first-passage-time p.d.f. through a constant boundary and for its Laplace transform are derived in terms of probability currents for a temporally homogeneous diffusion process. Ultimate absorption and recurrence problems are also considered. The moments of the first-passage time are finally explicitly obtained.
Age-dependent minimal repair
Authors: Block Henry W. , Borges Wagner S. , Savits Thomas H.
Published: April 2006

A stochastic model is developed to describe the operation in time of the following maintained system setting. A piece of equipment is put in operation at time 0. Each time it fails, a maintenance action is taken which, with probability p(t), is a complete repair or, with probability q(t)=1– p(t), is a minimal repair, where t is the age of the equipment in use at the failure time. It is assumed that complete repair restores the equipment to its good as new condition, that minimal repair restores the equipment to its condition just prior to failure and that both maintenance actions take negligible time.

If the equipment's life distribution F is a continuous function, the successive complete repair times are shown to be a renewal process with interarrival distribution

for t ≧ 0. Preservation and monotone properties of the model extending the results of Brown and Proschan (1983) are obtained.
Evolutionarily stable strategies in diploid populations with general inheritance patterns
Authors: Hines W. G. S. , Bishop D. T.
Published: April 2006

A simple argument demonstrates that the mean strategy of a diploid sexual population at evolutionary equilibrium can be expected to be an evolutionarily stable strategy (ESS) in the formal sense. This result follows under a wide set of models of genetic inheritance of strategy (including sexual selection) provided that the ESS is both attainable and maintainable.
The proportion of quadrilaterals formed by random lines in a plane
Authors: Tanner J. C.
Published: April 2006

An expression is derived for the proportion of quadrilaterals among the polygons formed by random lines in the plane. Its value is 0.381 466….
The first repetition of a pattern in a symmetric Bernoulli sequence
Authors: Karnin Ehud D.
Published: April 2006

In a symmetric sequence of Bernoulli trials we define each successive l outcomes as a pattern, and look at the first time that any pattern repeats. Asymptotic expressions, as l →∞, of the distribution and the expectation of this waiting time are derived.
On interarrival times in simple stochastic epidemic models
Authors: Yang Grace , Chiang C. L.
Published: April 2006

The probability distributions of the size and the duration of simple stochastic epidemic models are well known. However, in most instances, the solutions are too complicated to be of practical use. In this note, interarrival times of the infectives are utilized to study asymptotic distributions of the duration of the epidemic for a class of simple epidemic models. A brief summary of the results on simple epidemic models in terms of interarrival times is included.
Availability measures for coherent systems of separately maintained components
Authors: Baxter Laurence A.
Published: April 2006

A coherent system of components, the failure pattern of each of which being assumed to be modelled by an alternating renewal process, is considered. Formulae are derived for the probability that the system is available at a series of points and for the expected numbers of failures and repairs of the system in a fixed interval. It is shown how the model can be generalised to permit each component to exhibit partial availability in the failed state.
On a generalized finite-capacity storage model
Authors: Woolford Samuel W.
Published: April 2006

This paper considers a finite-capacity storage model defined on a Markov chain {Xn; n = 0, 1, ·· ·}, having state space J ⊆ {1, 2, ·· ·}. If Xn = j, then there is a random ‘input' Vn(j) (a negative input implying a demand) of ‘type' j, having a distribution function Fj(·). We assume that {Vn(j)} is an i.i.d. sequence of random variables, taken to be independent of {Xn} and of {Vn (k)}, for k ≠ j. Here, the random variables Vn(j) represent instantaneous ‘inputs' of type j for our storage model. Within this framework, we establish certain limit distributions for the joint processes (Zn, Xn) and (Zn, Qn, Ln), where Zn (defined in (1.2)) is the level of storage at time n, Qn (defined in (1.3)) is the cumulative overflow at time n, and Ln (defined in (1.4)) is the cumulative demand lost due to shortage of supply up to time n. In addition, an expression for the time-dependent distribution of (Zn, Xn) is obtained.
Conditioned limit theorems for waiting-time processes of the M/G/1 queue
Authors: Hooghiemstra G.
Published: April 2006

This paper is on conditioned weak limit theorems for imbedded waiting-time processes of an M/G/1 queue. More specifically we study functional limit theorems for the actual waiting-time process conditioned by the event that the number of customers in a busy period exceeds n or equals n. Attention is also paid to the actual waiting-time process with random time index.

Combined with the existing literature on the subject this paper gives a complete account of the conditioned limit theorems for the actual waiting-time process of an M/G/1 queue for arbitrary traffic intensity and for a rather general class of service-time distributions.

The limit processes that occur are Brownian excursion and meander, while in the case of random time index also the following limit occurs: Brownian excursion divided by an independent and uniform (0, 1) distributed random variable.
On the characterization of point processes with the order statistic property without the moment condition
Authors: Puri Prem S.
Published: April 2006

The paper characterizes point processes with the order statistic property without the unnecessary condition of finiteness of the first moment of the process, a condition imposed by previous researchers. It shows that the class of these processes is composed only of mixed Poisson processes up to a time-scale transformation and of the mixed sample processes. It also introduces a multivariate analog of the order statistic property and characterizes completely the class of multivariate point processes with this property.
Record values and extreme value distributions
Authors: Nagaraja H. N.
Published: April 2006

The limit distribution of thekth maximum from a random sample of sizenwhenn →∞ is identified as the distribution of thekth lower record value from one of three extreme value distributions. This fact is used in giving a different canonical representation and new proofs of the results of Hall (1978) for this limiting random variable. A characterization of the exponential distribution based on upper record values is given.
A solvable model for a finite-capacity queueing system
Authors: Giorno V. , Negri C. , Nobile A. G.
Published: April 2006

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.
On the busy-period distributions ofM/G/1/Kqueues by state-dependent arrivals and FCFS/LCFS-P service disciplines
Authors: Shanthikumar J. George , Sumita Ushio
Published: April 2006

The busy-period distributions ofM/G/1/Kqueues with state-dependent arrival rates are considered. Two recursion formulas for the Laplace–Stieltjes transforms of the busy periods under the FCFS and preempt resume LCFS service disciplines are obtained. It is shown that the busy-period distributions for the two service disciplines are, in general, different, in contrast to the fact that they coincide for ordinaryM/G/1 queues. For deterministic service times and arrival rates non-increasing in the number of customers in the system, stochastic ordering between these two busy periods is also established.
On stopping rules in proofreading
Authors: Chow Chung-Wen , Schechner Zvi
Published: April 2006

Stopping rules in the context of proofreading are studied. Previous results by Yang et al. [6] are corrected and a computational procedure to obtain an optimal rule is presented.
Bisexual Galton–Watson branching processes with superadditive mating functions
Authors: Daley D. J. , Hull David M. , Taylor James M.
Published: April 2006

For a bisexual Galton–Watson branching process with superadditive mating function there is a simple criterion for determining whether or not the process becomes extinct with probability 1, namely, that the asymptotic growth rate r should not exceed 1. When extinction is not certain (equivalently, r > 1), simple upper and lower bounds are established for the extinction probabilities. An example suggests that in the critical case that r = 1, some condition like superadditivity is essential for ultimate extinction to be certain. Some illustrative numerical comparisons of particular mating functions are made using a Poisson offspring distribution.
The non-renewal nature of the quasi-input process in theM/G/1/∞ queue
Authors: Hunter Jeffrey J.
Published: April 2006

Falin (1984) examined the quasi-input process (the flow of service starting times) in theM/G/1/∞ queue and raised the question as to whether this process is a renewal process. We show that, except in the trivial case of instantaneous service, the quasi-input process is never renewal.
On queues with periodic inputs
Authors: Bambos Nicholas , Walrand Jean
Published: April 2006

We consider a single-server queue with a periodic and ergodic input. It is shown that if the traffic intensity is less than 1, then the waiting time process is asymptotically periodic. Limit theorems associated with the asymptotic behavior of the queue are also proven. The results are then extended to acyclic networks of queues with periodic inputs. Particular cases of these results had been previously obtained for a single queue with periodic Poisson arrival input process and with independent and identically distributed service times.
Joint simulation of backward and forward recurrence times in a renewal process
Authors: Winter B. B.
Published: April 2006

It is shown that, in a renewal process with inter-arrival distribution F, an observation from the asymptotic (when t →∞) joint distribution of backward and forward recurrence times at t can be simulated by simulating an observation of the pair (UW, (1 – U)W), where U and W are independent random variables with U ~ uniform(0, 1) and W distributed according to the length-biased version of F.
Recursions and limit theorems for the strength and lifetime distributions of a fibrous composite
Authors: Kuo Chia-Chyuan , Phoenix S. Leigh
Published: April 2006

A composite material is a parallel arrangement of stiff brittle fibers in a flexible matrix. Under load fibers fail, and the loads of failed fibers are locally redistributed onto nearby survivors through the matrix. In this paper we develop a new technique for computing the probability of failure under a previously studied model of the failure process. A recursion and limit theorem are obtained which apply separately to static strength and fatigue lifetime depending on the composite loading and the probability model for the failure of individual fibers under their own loads. The limit theorem yields an approximation for the distribution function for composite lifetime which is of the form 1 – [1 – W(t)]mn where W(t) is a characteristic distribution function and mn is the composite volume, reflecting a size effect. A similar result holds also for static strength. In both cases such a result was conjectured several years ago. This limit theorem is obtained from the recursion upon applying a key theorem in the theory of the renewal equation. In the proofs three technical conditions arise which must be verified in specific applications. In the case of static strength these conditions are quite easy to verify, but in the case of fatigue lifetime the verification is generally difficult, and entails considerable numerical computation.
Optimal control of a finite dam: Wiener process input
Authors: Yeh Lam , Hua Lou Jiann
Published: April 2006

The problem of optimal control of a finite dam in the class of policies has been considered by Lam Yeh [6], [7]. In this paper, by using the first Dynkin formula, the same problems of specifying an optimal policy in the class of the policies to minimize the expected total discounted cost as well as the long-run average cost are considered. Both the expected total discounted cost and long-run average cost are determined explicitly, and then the optimal policy can be found numerically, Also, we obtain the transition density function and the resolvent operator of a reflecting Wiener process.
On the kinetics of multitype polymer reactions
Authors: Mellein B. , Vicente J. L.
Published: April 2006

A multitype polymer reaction process is considered. Its dynamics is described by means of the evolution in time of the average number of reactions (of any kind) and the mean number of unreacted chain segments (of any length), assuming that the initial chain molecule consists ofnunreacted units. The asymptotic behaviour (n→∞) of the variance of the extent of reaction is also studied.
Convergence of quasi-stationary to stationary distributions for stochastically monotone Markov processes
Authors: Pollak Moshe , Siegmund David
Published: April 2006

It is shown that if a stochastically monotone Markov process on [0,∞) with stationary distribution H has its state space truncated by making all states in [B,∞) absorbing, then the quasi-stationary distribution of the new process converges to H as B →∞.
Applied probability—past, present and future
Authors: Kendall David G.
Published: April 2006

After some reminiscences about the founding of the Applied Probability journals the author discusses three open problems concerned respectively with:

(i) the prehistory of applied probability

(ii) Poisson–Delauney Simplexes

(iii) voids and pancakes in the universe.
Some applications of weak convergence to statistics
Authors: Loynes R. M.
Published: April 2006

Results showing the weak convergence of certain stochastic processes are used to derive both known and new (asymptotic) properties of signs of residuals from regression; other weak convergence results are derived, and used to determine the behaviour of runs of residuals.
Homogeneous row-continuous bivariate markov chains with boundaries
Authors: Keilson J. , Zachmann M.
Published: April 2006

The matrix-geometric results of M. Neuts are extended to ergodic row-continuous bivariate Markov processes [J(t), N(t)] on state space B = {(j, n)} for which: (a) there is a boundary level N for N(t) associated with finite buffer capacity; (b) transition rates to adjacent rows and columns are independent of row level n in the interior of B. Such processes are of interest in the modelling of queue-length for voice-data transmission in communication systems.

One finds that the ergodic distribution consists of two decaying components of matrix-geometric form, the second induced by the finite buffer capacity. The results are obtained via Green's function methods and compensation. Passage-time distributions for the two boundary problems are also made available algorithmically.
The width of a spectral window
Authors: Hannan E. J. , Rissanen J.
Published: April 2006

A method is derived for choosing the width of a spectral window in spectrum estimation. The method is based upon the idea of minimising complexity, i.e. the length, in bits, of a code for the data.
On point processes on the circle
Authors: Hüsler Jürg
Published: April 2006

Point processes on the circle with circumference 1 are considered, which are related to the coverage problem of the circle by n randomly placed arcs of a fixed length. The anticlockwise endpoint of each arc is assumed to be uniformly distributed on the circle. We deal with a general limit result on the convergence of these point processes to a Poisson process on the circle. This result is then applied to several cases of the coverage problem, giving improved limit results in these cases. The proof uses a new convergence result of general point processes.
A planar random motion governed by the two-dimensional telegraph equation
Authors: Orsingher Enzo
Published: April 2006

In this paper a planar random motion governed by the two-dimensional telegraph equation is presented. It is proved that the particle performing motion is at any time t within a circle centred at the starting point and with radius . The explicit density of the particle position is obtained. Results concerning the trend of motion are also given.
Optimal estimation for semimartingales
Authors: Thavaneswaran A. , Thompson M. E.
Published: April 2006

This paper extends a result of Godambe's theory of parametric estimation for discrete-time stochastic processes to the continuous-time case. LetP={P} be a family of probability measures such that (Ω,F, P) is complete, (Ft, t≧0) is a standard filtration, andX = (XtFt, t ≧ 0)is a semimartingale for everyP ∈ P. For a parameterθ(Ρ), supposeXt=Vt,θ+Ht,θwhere theVθprocess is predictable and locally of bounded variation and theHθprocess is a local martingale. Consider estimating equations forθof the formprocess is predictable. Under regularity conditions, an optimal form forαθin the sense of Godambe (1960) is determined. WhenVt,θis linear inθthe optimal, corresponds to certain maximum likelihood or least squares estimates derived previously in special cases. Asymptotic properties of, are discussed.
The effect of increasing service rates in a closed queueing network
Authors: Shanthikumar J. George , Yao David D.
Published: April 2006

In this paper we study the equilibrium behavior of the queue lengths in a product-form closed queueing network when the service rates at a subset of stations (nodes) are increased. Univariate and multivariate likelihood ratio orderings as well as multivariate stochastic ordering of the queue lengths are established to indicate the effect of increasing the service rates. Relations among these orderings are also developed.
Coin tossing, revisited
Authors: Percus O. E. , Percus J. K.
Published: April 2006

An iterated sequence of Bernoulli trials is carried out and the success probability estimated at each point on the sequence by the current success ratio. We find the probability P1 that this estimate always lies above some pre-selected rational fraction p′, and its complement P2, the probability that it will reach p′ or below at least once. In the region p′ ≧ p, P1 = 0. In the region p′ < p, P1 ≠ 0 and is furthermore a discontinuous function of p′ at every rational p′.
Boundary crossing for moving sums
Authors: Glaz J. , Johnson B.
Published: April 2006

Let Xi, i ≧ 1, be a sequence of independent N(0, 1) random variables and Sj,m = Xj + · ·· + Xj+m–1, the jth moving sum. Let τ m = inf{j ≧ 1 : Sj,m > a} + m – 1, the boundary crossing time. Approximation in the spirit of Glaz and Johnson (1984), (1986) and Samuel-Cahn (1983) are given for Pr(τm > n), E(τ m), and σ (τ m),the standard deviation of τm.
Relationships and decomposition in the delayed bernoulli feedback queueing system
Authors: König D. , Miyazawa M.
Published: April 2006

For the delayed Bernoulli feedback queue with first come–first served discipline under weak assumptions a relationship for the generating functions of the joint queue-length distribution at various points in time is given. A decomposition for the generating function of the stationary total queue length distribution has been proven. The Laplace-Stieltjes transform of the stationary joint workload distribution function is represented by its marginal distributions. The arrival process is Poisson, renewal or arbitrary stationary, respectively. The service times can form an i.i.d. sequence at each queue. Different kinds of product form of the generating function of the joint queue-length distribution are discussed.
Monotone stopping games
Authors: Mamer John W.
Published: April 2006

We consider the extension of optimal stopping problems to non-zero-sum strategic settings called stopping games. By imposing a monotone structure on the pay-offs of the game we establish the existence of a Nash equilibrium in non-randomized stopping times. As a corollary, we identify a class of games for which there are Nash equilibria in myopic stopping times. These games satisfy the strategic equivalent of the classical ‘monotone case' assumptions of the optimal stopping problem.
Non-random shuffling for multiple decks
Authors: Gottlieb Gary
Published: April 2006

Non-randomness that arises in the shuffling of multiple numbers of decks of playing cards is modeled. An efficient way to exploit the non-randomness is derived, and its effect on the win rate for a simple game of chance is derived.
On the convex hull of random points in a polytope
Authors: Dwyer Rex A.
Published: April 2006

The convex hull of n points drawn independently from a uniform distribution on the interior of a d-dimensional polytope is investigated. It is shown that the expected number of vertices is O(logd–1n) for any polytope, the expected number of vertices is Ω(logd–1n) for any simple polytope, and the expected number of facets is O(logd–1n) for any simple polytope. An algorithm is presented for constructing the convex hull of such sets of points in linear average time.
The identification of ARMA processes
Authors: Hong-Zhi An , Zhao-Guo Chen
Published: April 2006

This paper presents a review of recent results for the identification of ARMA processes according to the principles introduced by Akaike, i.e. assuming that the true orders exist and proposing criteria such as AIC and BIC. The development both of these methods and of consistency theory has been led by E. J. Hannan.
Consistency of model selection and parameter estimation
Authors: Shibata Ritei
Published: April 2006

The relationship between consistency of model selection and that of parameter estimation is investigated. It is shown that the consistency of model selection is achieved at the cost of a lower order of consistency of the resulting estimate of parameters in some domain. The situation is different when selecting autoregressive moving average models, since the information matrix becomes singular when overfitted. Some detailed analyses of the consistency are given in this case.
A simultaneous test in the presence of nested alternative hypotheses
Authors: Hosoya Yuzo
Published: April 2006

This paper considers the generalized likelihood ratio (GLR) test or its modification dealing with nested models. The algorithm for evaluating the critical values and the error-rates for the canonical tests are provided; a table of critical values of a class of GLR tests is also given. The test proposed in the paper has applications in time-series model selection.
The Box-Jenkins approach to random coefficient autoregressive modelling
Authors: Nicholls D. F.
Published: April 2006

Recent time series research has been directed towards the relaxation of the assumption that time series models have constant coefficients. One class of models to emerge as a result of this has been that of random coefficient autoregressive models. This paper demonstrates how the Box-Jenkins three-step approach of model specification, estimation and diagnostic checking may be applied to this class of models.
An algorithm for exponential fitting revisited
Authors: Osborne M. R. , Smyth G. K.
Published: April 2006

An algorithm for exponential fitting is presented which exploits the separable regression structure and a reparametrization. The algorithm has proved very satisfactory, and theoretical reasons for this are developed.
On the Extinction of theS–I–Sstochastic logistic epidemic
Authors: Kryscio Richard J. , Lefèvre Claude
Published: April 2006

We obtain an approximation to the mean time to extinction and to the quasi-stationary distribution for the standardS–I–Sepidemic model introduced by Weiss and Dishon (1971). These results are a combination and extension of the results of Norden (1982) for the stochastic logistic model, Oppenheim et al. (1977) for a model on chemical reactions, Cavender (1978) for the birth-and-death processes and Bartholomew (1976) for social diffusion processes.
A symmetry-based constructive approach to probability densities for one-dimensional diffusion processes
Authors: Giorno V. , Nobile A. G. , Ricciardi L. M.
Published: April 2006

Special symmetry conditions on the transition p.d.f. of one-dimensional time-homogeneous diffusion processes with natural boundaries are investigated and exploited to derive closed-form results concerning the transition p.d.f.'s in the presence of absorbing and reflecting boundaries and the first-passage-time p.d.f. through time-dependent boundaries.
Stability of extremes with random sample size
Authors: Voorn W. J.
Published: April 2006

A non-degenerate distribution function F is called maximum stable with random sample size if there exist positive integer random variables Nn, n = 1, 2, ···, with P(Nn = 1) less than 1 and tending to 1 as n → ∞ and such that F and the distribution function of the maximum value of Nn independent observations from F (and independent of Nn) are of the same type for every index n. By proving the converse of an earlier result of the author, it is shown that the set of all maximum stable distribution functions with random sample size consists of all distribution functions F satisfying

where c2, c3, · ·· are arbitrary non-negative constants with 0 < c2 + c3 + · ·· <∞, and all distribution functions G and H defined by F(x)= G(c + exp(x)) and F(x) = H(c – exp(–x)), –∞ < x <∞, where c is an arbitrary real constant.
The rate of convergence of the vector of variances and covariances in non-homogeneous Markov systems
Authors: Vassiliou P.-C. G. , Tsaklidis G.
Published: April 2006

The aims of this paper are twofold. The first is to study the rate of convergence of the sequence of vectors of expectations, variances and covariances in NHMS. It is proved that under certain conditions easily met in practice the rate is geometric. The second is to study the rate of convergence of the same sequence when the NHMS is under cyclic behaviour and it is also proved that the rate of convergence of the d subsequences (d being the period of the cycle) in which the sequence splits is geometric.
Looking forwards and backwards in a bisexual moran model
Authors: Kämmerle K.
Published: April 2006

In this paper a bisexual Moran model is introduced. The population consists of N pairs of individuals. At times t = 1, 2, ·· ·two individuals are born, who ‘choose their parents randomly' and independently of each other. Then one of the pairs is removed and replaced by the two individuals born at that instant.

The extinction probability of the descendants of a single pair and the number of ancestors of a whole generation are studied. A limit result for large population sizes has been derived by diffusion approximation methods.
Linear growth in near-critical population-size-dependent multitype Galton–Watson processes
Authors: Klebaner Fima C.
Published: April 2006

We consider a multitype population-size-dependent branching process in discrete time. A process is considered to be near-critical if the mean matrices of offspring distributions approach the mean matrix of a critical process as the population size increases. We show that if the second moments of offspring distributions stabilize as the population size increases, and the limiting variances are not too large in comparison with the deviation of the means from criticality, then the extinction probability is less than 1 and the process grows arithmetically fast, in the sense that any linear combination which is not orthogonal to the left eigenvector of the limiting mean matrix grows linearly to a limit distribution. We identify cases when the limiting distribution is gamma. A result on transience of multidimensional Markov chains is also given.
The hazard and vitality measures of ageing
Authors: Kupka Joseph , Loo Sonny
Published: April 2006

A new measure of the ageing process called the vitality measure is introduced. It measures the ‘vitality' of a time period in terms of the increase in average lifespan which results from surviving that time period. Apart from intrinsic interest, the vitality measure clarifies the relationship between the familiar properties of increasing hazard and decreasing mean residual life. The main theorem asserts that increasing hazard is equivalent to the requirement that mean residual life decreasesfasterthan vitality. It is also shown for general (i.e. not necessarily absolutely continuous) distributions that the properties of increasing hazard, increasing failure rate, and increasing probability of ‘sudden death' are all equivalent.
Modified Lindley process with replacement: dynamic behavior, asymptotic decomposition and applications
Authors: Shanthikumar J. George , Sumita Ushio
Published: April 2006

We consider a discrete-time stochastic process {Wn,n≧0} governed by i.i.d random variables {ξn} whose distribution has support on (–∞,∞) and replacement random variables {Rn} whose distributions have support on [0,∞). GivenWn, Wn+ 1takes the valueWn+ζn+ 1if it is non-negative. OtherwiseWn+ 1takes the valueRn +1where the distribution ofRn+ 1depends only on the value ofWn+ ζn +1.This stochastic process is reduced to the ordinary Lindley process forGI/G/1 queues whenRn= 0 and is called a modified Lindley process with replacement (MLPR). It is shown that a variety of queueing systems with server vacations or priority can be formulated as MLPR. An ergodic decomposition theorem is given which contains recent results of Doshi (1985) and Keilson and Servi (1986) as special cases, thereby providing a unified view.
The distributional structure of finite moving-average processes
Authors: McKenzie ED
Published: April 2006

Analysis of time-series models has, in the past, concentrated mainly on second-order properties, i.e. the covariance structure. Recent interest in non-Gaussian and non-linear processes has necessitated exploration of more general properties, even for standard models. We demonstrate that the powerful Markov property which greatly simplifies the distributional structure of finite autoregressions has an analogue in the (non-Markovian) finite moving-average processes. In fact, all the joint distributions of samples of aqth-order moving average may be constructed from only the (q+ 1)th-order distribution. The usefulness of this result is illustrated by references to three areas of application: time-reversibility; asymptotic behaviour; and sums and associated point and count processes. Generalizations of the result are also considered.
On Cox processes and gamma renewal processes
Authors: Yannaros Nikos
Published: April 2006

It is shown that the gamma distribution with shape parameter α can be obtained through ap-thinning for every 0
 1, the gamma distribution cannot be obtained through thinning. The class of renewal processes with gamma-distributed times between events is considered. It is shown that an ordinary gamma renewal process is a Cox process if and only if 0 < α ≦ 1. Necessary and sufficient conditions for delayed gamma renewal processes to be Cox are also given. Finally, a short description of the gamma renewal process as a Cox process is given.
Asymptotic behavior of Hill's estimate and applications
Authors: Lo Gane Samb
Published: April 2006

The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number was shown to be a characteristic of distribution functions belonging to the Fréchet domain of attraction (Mason (1982)). As a contribution to a complete theory of inference for the upper tail of a general distribution function, we give the asymptotic behavior (weak and strong) of Hill's estimate when the associated distribution function belongs to the Gumbel domain of attraction. Examples, applications and simulations are given.
Tangential measure on the set of convex infinite cylinders
Authors: Molter Ursula Maria
Published: April 2006

We find a ‘natural' measure on the set of convex infinite cylinders touching a convex body K in En. Using the curvature measures, we can calculate the probability that a convex infinite cylinder and a convex body K are tangent in some previously determined regions. As a particular case we obtain a measure on all q-planes touching K.
Necessary and sufficient conditions for stability of a bin-packing system
Authors: Courcoubetis C. , Weber R. R.
Published: April 2006

Objects of various integer sizes, o1, · ··, on, are to be packed together into bins of size N as they arrive at a service facility. The number of objects of size oi which arrive by time t is , where the components of are independent renewal processes, with At/t → λ as t → ∞. The empty space in those bins which are neither empty nor full at time t is called the wasted space and the system is declared stabilizable if for some finite B there exists a bin-packing algorithm whose use guarantees the expected wasted space is less than B for all t. We show that the system is stabilizable if the arrival processes are Poisson and λ lies in the interior of a certain convex polyhedral cone Λ. In this case there exists a bin-packing algorithm which stabilizes the system without needing to know λ. However, if λ lies on the boundary of Λ the wasted space grows as and if λ is exterior to Λ it grows as O(t); these conclusions hold even if objects may be repacked as often as desired.
The extinction probability of descendants in bisexual models of fixed population size
Authors: Kämmerle K.
Published: April 2006

In this paper exchangeable bisexual models with fixed population size and non-overlapping generations are introduced. Each generation consists of N pairs of individuals. The pairs of a generation have altogether 2N children. These individuals form randomly the N pairs of the next generation. The extinction probability of the descendants of a fixed number of pairs of generation 0 is discussed. Under suitable conditions it can be approximately described by the extinction probability of a Galton–Watson process, if the population size is large. Special examples are a bisexual Wright–Fisher model and models with a uniformly bounded number of children of a pair.
Modelling heterogeneity in survival data
Authors: Hougaard Philip
Published: April 2006

Ordinary survival models implicitly assume that all individuals in a group have the same risk of death. It may, however, be relevant to consider the group as heterogeneous, i.e. a mixture of individuals with different risks. For example, after an operation each individual may have constant hazard of death. If risk factors are not included, the group shows decreasing hazard. This offers two fundamentally different interpretations of the same data. For instance, Weibull distributions with shape parameter less than 1 can be generated as mixtures of constant individual hazards. In a proportional hazards model, neglect of a subset of the important covariates leads to biased estimates of the other regression coefficients. Different choices of distributions for the unobserved covariates are discussed, including binary, gamma, inverse Gaussian and positive stable distributions, which show both qualitative and quantitative differences. For instance, the heterogeneity distribution can be either identifiable or unidentifiable. Both mathematical and interpretational consequences of the choice of distribution are considered. Heterogeneity can be evaluated by the variance of the logarithm of the mixture distribution. Examples include occupational mortality, myocardial infarction and diabetes.
On identifiability in the autopsy model of reliability theory
Authors: Antoine Robin , Doss Hani , Hollander Myles
Published: April 2006

A coherent system is observed until it fails. At the instant of system failure, the set of failed components and the failure time of the system are noted. The failure times of the components are not known. We consider whether the component life distributions can be determined from the distributions of the observed data.

Meilijson (1981) gave a condition on the structure of the system that was sufficient for the identifiability of the component distributions, under the assumption that the component life distributions are continuous and have common essential extrema. Nowik (1990) gave necessary and sufficient conditions for identifiability under the more restrictive condition that the component distributions have atoms at their common essential infimum and are mutually absolutely continuous. We give a necessary condition for identifiability, which we show to be equivalent to Nowik's condition, under the assumption that the distributions are continuous and strictly increasing. We derive a sufficient condition for identifiability, more general than Meilijson's, for the case in which the component distributions are assumed to be analytic. We also show that our necessary condition for identifiability is both necessary and sufficient when the component life distributions are assumed to belong to certain parametric families.
Poisson approximation for some epidemic models
Authors: Ball Frank , Barbour A. D.
Published: April 2006

The Daniels' Poisson limit theorem for the final size of a severe general stochastic epidemic is extended to the Martin-Löf epidemic, and an order of magnitude for the error in the approximation is also given. The argument consists largely of showing that the number of survivors of a severe epidemic is essentially the same as the number of isolated vertices in a random directed graph. Poisson approximation for the latter quantity is proved using the Stein–Chen method and a suitable coupling.
On the GIX/G/∞ system
Authors: Liu L. , Kashyap B. R. K. , Templeton J. G. C.
Published: April 2006

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.
A paradox of congestion in a queuing network
Authors: Cohen Joel E. , Kelly Frank P.
Published: April 2006

In an uncongested transportation network, adding routes and capacity to an existing network must decrease, or at worst not change, the average time individuals require to travel through the network from a source to a destination. Braess (1968) discovered that the same is not true in congested networks. Here we give an example of a queuing network in which added capacity leads to an increase in the mean transit time for everyone. Self-seeking individuals are unable to refrain from using the additional capacity, even though using it leads to deterioration in the mean transit time. This example appears to be the first queuing network to demonstrate the general principle that in non-co-operative games with smooth payoff functions, user-determined equilibria generically deviate from system-optimal equilibria.
On the system queue length distributions of LCFS-P queues with arbitrary acceptance and restarting policies
Authors: Miyazawa Masakiyo
Published: April 2006

Shanthikumar and Sumita (1986) proved that the stationary system queue length distribution just after a departure instant is geometric forGI/GI/1 with LCFS-P/H service discipline and with a constant acceptance probability of an arriving customer, where P denotes preemptive and H is a restarting policy which may depend on the history of preemption. They also got interesting relationships among characteristics. We generalize those results forG/G/1 with an arbitrary restarting LCFS-P and with an arbitrary acceptance policy. Several corollaries are obtained. Fakinos' (1987) and Yamazaki's (1990) expressions for the system queue length distribution are extended. For a Poisson arrival case, we extend the well-known insensitivity for LCFS-P/resume, and discuss the stationary distribution for LCFS-P/repeat.
Empirical Laplace transform and approximation of compound distributions
Authors: Csörgő Sándor , Teugels Jef L.
Published: April 2006

Let be i.i.d. non-negative random variables with d.f. F and Laplace transform L. Let N be integer valued and independent of In many applications one knows that for y → ∞ and a function φ
where in turn τ is the solution of an equation

On the basis of a sample of size n we derive an estimator τ n for τ by solving ψ (τ n, Ln(τ n), L′n(τ n), · ··) = 0 where Ln is the empirical version of L. This estimator is then used to derive the asymptotic behaviour of φ (y, τ n, Ln(τ n), L′n(τ n), · ··). We include five examples, some of which are taken from insurance mathematics.
Asymptotic distribution of the maximum of n independent stochastic processes
Authors: Balkema A. A. , De Haan L. , Karandikar R. L.
Published: April 2006

Limits in distribution of maxima of independent stochastic processes are characterized in terms of spectral functions acting on a Poisson point process.
A coupling of finite particle systems
Authors: Mountford T. S.
Published: April 2006

We show that for a large class of one-dimensional interacting particle systems, with a finite initial configuration, any limit measure , for a sequence of times tending to infinity, must be invariant. This result is used to show that the one-dimensional biased annihilating branching process with parameter > 1/3 converges in distribution to the upper invariant measure provided its initial configuration is almost surely finite and non-null.
A note on a D/G/K loss system with retrials
Authors: Pourbabai Behnam
Published: April 2006

An algorithm is suggested for approximating the performance of a D/G/K loss system with deterministic input, generally distributed processing time, K heterogeneous servers, the random access processing discipline, and retrials in steady state. In loss systems with retrials, the units which at the instants of their arrival at the system find all the servers busy, are not lost: those units retry to be processed by merging with the incoming arrival units. In this system, a fraction of the units which have not initially been processed will be allowed to leave the system. The performance of this system in steady state is approximated by a recursive technique.
Asymptotic results for a problem of DNA breakage
Authors: Cowan Richard , Culpin David , Gates David
Published: April 2006

Double-stranded DNA molecules can be damaged by enzymic action or radiation, in a manner which creates randomly-located single-stranded breaks (nicks). The accumulation of these leads eventually to the double-stranded breakage of the molecule, because two opposite-strand nicks within a critical distance of each other establish conditions for breakage. We study the random variable N, defined as the number of nicks needed for double-stranded breakage to occur. We develop an asymptotic theory which is needed for practical computations.
Dispersive ordering by dilation
Authors: Muñoz-Perez J. , Sanchez-Gomez A.
Published: April 2006

In this paper a necessary and sufficient condition for the dispersive ordering in dilation sense is given by a convex function which is called the dispersive function and characterizes the distribution function. Some interesting properties of the ordering follow from this result.
On the relation between partial balance and insensitivity
Authors: Fakinos D.
Published: April 2006

Direct and simple proofs are given of the equivalence of partial balance over a set of states and the fact that the corresponding equilibrium distribution is insensitive to nominal sojourn time in that set and independent of its past and remaining duration. By a counter-example it is shown that solely insensitivity is not sufficient for partial balance.
Convexity results for single-server queues and for multiserver queues with constant service times
Authors: Harel Arie
Published: April 2006

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates.

These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).
Bounds for discounted stochastic scheduling problems
Authors: Glazebrook K. D.
Published: April 2006

Suppose that π is a policy for resource allocation in a stochastic environment andπ ∗is an optimal policy. Two existing procedures for policy evaluation are described and compared. Both of these evaluateπby means of upper bounds onR(π ∗)– R(π), the total reward lost when making resource allocations according toπrather than π∗. The bounds developed by these two methods are called Type 1 and Type 2. We demonstrate by example that neither of these procedures dominates the other in the sense of always yielding tighter bounds. A modification to Type 2 bounds is proposed resulting in an improved procedure which always dominates the Type 1 approach.
The Gillis–Domb–Fisher correlated random walk
Authors: Chen Anyue , Renshaw Eric
Published: April 2006

Correlated random walk models figure prominently in many scientific disciplines. Of fundamental importance in such applications is the development of the characteristic function of then-step probability distribution since it contains complete information on the probability structure of the process. Using a simple algebraic lemma we derive then-step characteristic function of the Gillis correlated random walk together with other related results. In particular, we present a new and simple proof of Gillis's conjecture, consider the generalization to the Gillis–Domb–Fisher walk, and examine the effect of including an arbitrary initial distribution.
Some results on block replacement policies and renewal theory
Authors: Shaked Moshe , Zhu Haolong
Published: April 2006

Age and block replacement policies are commonly used in order to reduce the number of in-service failures. The focus in this paper is on the block replacement policies, about which relatively less is known than age replacement policies. Several new results which connect the properties of block replacement policies with the properties of the corresponding renewal function and the excess lifetimes are obtained. Some applications and the relationships between these new results and some known results are included.