bluuebunny/crossref_metadata_2025_split huggingface dataset:
On identifiability in the autopsy model of reliability theory
Authors: Antoine Robin , Doss Hani , Hollander Myles 
Published: July 2016

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.
A note on seasonal Markov chains with gamma or gamma-like distributions
Authors: Lloyd E. H. , Saleem S. D. 
Published: July 2016

Weighted sums defined on a Markov chain (MC) are important in applications (e.g. to reservoir storage theory). The rather intractable theory of such sums simplifies to some extent when the transition p.d.f. of the chain {Xt
} has a Laplace transform (LT) L(Xt

+1; θ |Χ t=x) of the ‘exponential' form H(θ) exp{ – G(θ)x}. An algorithm is derived for the computation of the LT of Σat,Χ t
for this class, and for a seasonal generalization of it.
A special case of this desirable exponential type of transition LT for a continuous-state discrete-time MC is identified by comparison with the LT of the Bessel distribution. This is made the basis for a new derivation of a gamma-distributed MC proposed by Lampard (1968).
A seasonal version of this process is developed, valid for any number of seasons.
Reference is made to related chains with three-parameter gamma-like distributions (of the Kritskii–Menkel family) that may be generated from the above by a simple power transformation.
Conditional moments in a critical age-dependent branching process
Authors: Weiner Howard J. 
Published: July 2016

Let X(t), N(t) respectively denote the number of cells alive at t and the total number of cells born by t in a critical age-dependent Bellman-Harris branching process.
The asymptotic behavior of the conditional moments, for 0 &lt; α ≦ 1, E(Nn
(αt) | X(t) &gt; 0), E(Nn
(t) |X(αt) &gt; 0), is obtained.
A diffusion approximation for correlation in queues
Authors: Woodside C. M. , Pagurek B. , Newell G. F. 
Published: July 2016

A diffusion model is used to find heavy traffic approximate autocorrelation functions for several variables in queueing systems (i.e. for waiting time, system time, number in system and unfinished work). A table is given by which correlations can easily be found for each variable in anyGI/G/1 queue. Further, the infinite sum or integral of the autocorrelations is also found, and the spectral density function. The sum has applications in statistical analysis of queues.Extensive comparisons of approximate and exact correlations and their sums are reported, particularly for waiting times and system times, but also including number in system inM/M/1 queues. In general the correlations have similar accuracy to the probability distributions found by diffusion approximations. The percentage error is less for number in system than for waiting time.
On the classical Bonferroni inequalities and the corresponding Galambos inequalities
Authors: Walker A. M. 
Published: July 2016

Let (A
1
A
2, · ··, An
) be a set of n events on a probability space. Let be the sum of the probabilities of all intersections of r events, and Mn
the number of events in the set which occur. The classical Bonferroni inequalities provide upper and lower bounds for the probabilities P(Mn
= m), and equal to partial sums of series of the form which give the exact probabilities. These inequalities have recently been extended by J. Galambos to give sharper bounds.
Here we present straightforward proofs of the Bonferroni inequalities, using indicator functions, and show how they lead naturally to new simple proofs of the Galambos inequalities.
Inspection times for stand-by units
Authors: Parmigiani Giovanni 
Published: July 2016

This paper studies optimal timing of inspections for units in cold stand-by. The problem is approached in continuous time. The policies developed adapt optimally to information provided by failures of the main unit and by ageing of both the standby and the main unit.Results include a general form for the optimal policy, consisting of a recursive relation between successive inspection times, and of a renewal-type integral equation to determine the value of the objective function for a given policy. Further results are derived for the case in which the failure densities describing the process are logconcave. Then the stopping rule is easily characterized. It is also shown that the interval between inspections decreases with time, and that the optimal schedule is unique. A binary search algorithm for finding the solution is outlined.
The stability of storage models with shot noise input
Authors: Lund Robert B. 
Published: July 2016

We examine the existence of limiting behavior, or stability, for storage models with shot noise input and general release rules. The shot noise feature of the input process allows the individual inputs to gradually enter the store.
We first show that a store under the unit release rule is stable if and only if the traffic intensity is less than one; this extends the classic result of Prabhu (1980) to the case of shot noise input. The stability of the unit release rule store and various stochastic orderings are then used to derive a sufficient condition for a store with a general release rule to be stable. Finally, we show that when restricted to a compact state space, our storage model is always stable.
An important component of the paper is the methodology employed: coupling and stochastic monotonicity play a key role in analyzing the non-Markov processes encountered.
Stochastic differential equations for ruin probabilities
Authors: Møller Christian Max 
Published: July 2016

The present paper proposes a general approach for finding differential equations to evaluate probabilities of ruin in finite and infinite time. Attention is given to real-valued non-diffusion processes where a Markov structure is obtainable. Ruin is allowed to occur upon a jump or between the jumps. The key point is to define a process of conditional ruin probabilities and identify this process stopped at the time of ruin as a martingale. Using the theory of marked point processes together with the change-of-variable formula or the martingale representation theorem for point processes, we obtain differential equations for evaluating the probability of ruin.
Numerical illustrations are given by solving a partial differential equation numerically to obtain the probability of ruin over a finite time horizon.
A proof of optimality for age replacement policies
Authors: Berg Menachem 
Published: July 2016

A well-known maintenance procedure for stochastically failing units is the age replacement policy (ARP). Under the ARP a unit is replaced on failure, or when it reaches a predetermined critical age.
In previous papers concerned with this procedure the authors searched for the optimal critical age to minimize the objective function under discussion. The purpose of this paper is to prove that the ARP itself is the optimal decision rule amongst all reasonable policies.
A queueing network analysis of dynamic reconfigurability in a hierarchical information network
Authors: Bhat U. Narayan , Nance Richard E. 
Published: July 2016

Hierarchical information networks are important in applications where the information management must support an existing tree-structured organization. Embedded computer-communication systems in military applications, with a dominant hierarchical command structure, are the most prominent examples. Also typical of such applications is the variability in message demand (both sources and intensity) depending on the external conditions encountered by the encapsulating system (the system supported by the embedded computer-communication system). Using a queueing network model for a hierarchical information network, we compare the effect of limited dynamic reconfiguration on expected transmission delays. The limited reconfigurability takes the form of apex transition among a proper subset of the communication nodes designated as the apex candidate set. Each apex candidate can assume the ultimate position under designated conditions. This network architecture is called a dynamic hierarchy. The model includes N + 1 nodes (0, …, N) with 0 identifying the apex node. We assume that message processing at each node is described by an M/M/1 model (single server with Poisson arrivals and exponential service times). Further message transfers among the nodes are served by communication links which also behave as M/M/1 queues.
Two distinctive features characterize the queueing network model:
1. The assignment of a set of weights to the nodes dependent on the hierarchical level reflects the increasing importance of information as it is transferred to higher levels.
2. The dynamic hierarchy requires a communications protocol that partitions the analysis of network delay into three periods: regular operation, reconfiguration, and adjustment. Characterization of the performance of the dynamic hierarchy entails the description of message transmission delay as a composite of the three periods.
Aspects of Lagrangian probability distributions
Authors: Sibuya Masaaki , Miyawaki Norihiko , Sumita Ushio 
Published: July 2016

Lagrangian distributions are reviewed from the viewpoint of the Galton-Watson process. They are related to the busy period in queuing systems and to the first visit in random walks.
A property of the distributions is remarked for the application to vacant vehicles in a new transit system. Combinatorial identities of multinomial and binomial coefficients and related recurrences are shown by a probabilistic method. Based on the identities and recurrences, random forests generated by the Poisson and geometric Galton-Watson processes are characterized.
Approximating last-exit probabilities of a random walk, by application to conditional queue length moments within busy periods of M/GI/1 queues
Authors: Daley D. J. , Servi L. D. 
Published: July 2016

Certain last-exit and first-passage probabilities for random walks are approximated via a heuristic method suggested by a ladder variable argument. They yield satisfactory approximations of the first- and second-order moments of the queue length within a busy period of an M/D/1 queue. The approximation is applied to the wider class of random walks that arise in studying M/GI/1 queues. For gamma-distributed service times the queue length distribution is independent of the arrival rate. For other distributions where the arrival rate affects the queue length distribution, we have to use conjugate distributions in order to exploit a local central limit property. The limit underlying the approximation has the nature of a Brownian excursion.
The source of the problem lies in recent queueing inference work; the connection with Takács' interests comes from both queueing theory and the ballot theorem.
Applications of the hazard rate ordering in reliability and order statistics
Authors: Boland Philip J. , El-Neweihi Emad , Proschan Frank 
Published: July 2016

The hazard rate ordering is an ordering for random variables which compares lifetimes with respect to their hazard rate functions. It is stronger than the usual stochastic order for random variables, yet is weaker than the likelihood ratio ordering. The hazard rate ordering is particularly useful in reliability theory and survival analysis, owing to the importance of the hazard rate function in these areas. In this paper earlier work on the hazard rate ordering is reviewed, and extensive new results related to coherent systems are derived. Initially we fix the form of a coherent structure and investigate the effect on the hazard rate function of the system when we switch the lifetimes of its components from the vector (T
1, · ··, Tn
) to the vector (T′
1, · ··, T′n
), where the hazard rate functions of the two vectors are assumed to be comparable in some sense. Although the hazard rate ordering is closed under the formation of series systems, we see that this is not the case for parallel systems even when the system is a two-component parallel system with exponentially distributed lifetimes. A positive result shows that for two-component parallel systems with proportional hazards (λ
1
r(t), λ
2
r(t))), the more diverse (λ
1, λ2
) is in the sense of majorization the stronger is the system in the hazard rate ordering. Unfortunately even this result does not extend to parallel systems with more than two components, demonstrating again the delicate nature of the hazard rate ordering.
The principal result of the paper concerns the hazard rate ordering for the lifetime of a k-out-of-n system. It is shown that if τ k|n
is the lifetime of a k-out-of-n system, then τ k|n
is greater than τ k+

1|n
in the hazard rate ordering for any k. This has an interesting interpretation in the language of order statistics. For independent (not necessarily identically distributed) lifetimes T
1, · ··, Tn
, we let Tk:n
represent the kth order statistic (in increasing order). Then it is shown that Tk +

1:n
is greater than Tk:n
in the hazard rate ordering for all k = 1, ···, n − 1. The result does not, however, extend to the stronger likelihood ratio order.
Weak limit for the stationary distribution of the infinite-alleles model
Authors: Avni Haim 
Published: July 2016

The limit behavior of the stationary distribution of the infinite-alleles model is reduced to a single Laplace transform formula. Some known results, such as Ewens' sampling formula, the distribution of the order-statistics and the frequency spectrum density are shown to follow from this relation. All the results are obtained within the framework of the configuration process, without recourse to finite alleles models.
In view of some recent results by Kingman (1977), the results apply wherever the Ewens' sampling formula is valid.
A limit theorem for patch sizes in a selectively-neutral migration model
Authors: Sawyer Stanley 
Published: July 2016

Assume a population is distributed in an infinite lattice of colonies in a migration and random mating model in which all individuals are selectively equivalent. In one and two dimensions, the population tends in time to consolidate into larger and larger blocks, each composed of the descendants of a single initial individual. LetN(t) be the (random) size of a block intersecting a fixed colony at timet.ThenE[N(t)] grows like √tin one dimension,t/logtin two, andtin three or more dimensions. On the other hand, each block by itself eventually becomes extinct. In two or more dimensions, we prove thatN(t)/E[N(t)] has a limiting gamma distribution, and thus the mortality of blocks does not make the limiting distribution ofN(t) singular. Results are proven for discrete time and sketched for continuous time.If a mutation rateu&gt; 0 is imposed, the ‘block structure' has an equilibrium distribution. IfN(u) is the size of a block intersecting a fixed colony at equilibrium, then asu→ 0N(u)/E[N(u)] has a limiting exponential distribution in two or more dimensions. In biological systemsu≈ 10–6is usually quite small.The proofs are by using multiple kinship coefficients for a stepping stone population.
The limiting behaviour of the maximal spacing generated by an i.i.d. sequence of Gaussian random variables
Authors: Deheuvels Paul 
Published: July 2016

LetMnbe the maximal spacing generated in the sample's range byΧ1,· ··,Χn, independent and identically distributed Gaussian N(0, 1) random variables. We obtain the limiting distribution ofand show thataccording to whether ε&gt; 0 orε&lt; 0.
Exponential ergodicity in Markov renewal processes
Authors: Teugels Jozef L. 
Published: July 2016

In [3], Kendall proved a solidarity theorem for irreducible denumerable discrete time Markov chains. Vere-Jones refined Kendall's theorem by obtaining uniform estimates [14], while Kingman proved analogous results for an irreducible continuous time Markov chain [4], [5].
We derive similar solidarity theorems for an irreducible Markov renewal process. The transient case is discussed in Section 3, and Section 4 deals with the positive recurrent case. Recently Cheong also proved solidarity theorems for Semi-Markov processes [1]. His theorems use the Markovian structure, while our emphasis is on the renewal aspects of Markov renewal processes.
An application to the M/G/1 queue is included in the last section.
Linear programming and continuous markovian decision problems
Authors: Mine Hisashi , Tabata Yoshio 
Published: July 2016

Summary
This paper is concerned with a continuous time parameter Markovian sequential decision process, and presents a method which transforms a given continuous parameter problem into a discrete one. It is proved that the optimal stationary policy for the resulting discrete time parameter Markovian decision process is also the optimal stationary policy for the original continuous one, and vice versa. The resulting discrete parameter problem may be more easily solved than the continuous one by applying the linear programming method. A simple numerical example is presented.
A single server tandem queue
Authors: Nair Sreekantan S. 
Published: July 2016

Avi-Itzhak, Maxwell and Miller (1965) studied a queueing model with a single server serving two service units with alternating priority. Their model explored the possibility of having the alternating priority model treated in this paper with a single server serving alternately between two service units in tandem.
Here we study the distribution of busy period, virtual waiting time and queue length and their limiting behavior.
Some applications of the theory of infinite capacity service systems to a single server system with linearly state dependent service
Authors: Conolly B. W. 
Published: July 2016

Summary
A certain single server queueing system with negative exponential service with mean rate nμ, when the system contains n customers, and Poisson arrivals, is formally equivalent to the infinite capacity system M/M/∞. This equivalence is exploited to yield in a very simple manner results for the single server system which were previously obtained by difficult analysis (see Hadidi (1969)).
Approximate distributions of Student's t-statistics for autoregressive coefficients calculated from regression residuals
Authors: Durbin J. 
Published: July 2016

We consider a multiple regression model in which the regressors are Fourier cosine vectors. These regressors are intended as approximations to ‘slowly changing' regressors of the kind often found in time series regression applications. The errors in the model are assumed to be generated by a special type of autoregressive model defined so that the regressors are eigenvectors of the quadratic forms occurring in the exponent of the probability density of the errors. This autoregression is intended as an approximation to the usual stationary autoregression. Both approximations are adopted for the sake of mathematical convenience.
Student's t-statistics are constructed for the autoregressive coefficients in a manner analogous to ordinary regression. It is shown that these statistics are distributed as Student's t to the first order of approximation, that is with errors in the density of order T
−1/2, where T is the sample size, while the squares of the statistics are distributed as the square of Student's t to the second order of approximation, that is with errors in the density of order Τ
–1.
Regression for randomly sampled spatial series: the trigonometric case
Authors: Brillinger David R. 
Published: July 2016

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j
in a subset of Rp
and θ is a finite-dimensional parameter. The particular cases of

0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j
} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.
Contributions of the paper include: study of the Rp
case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j
} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.
Point-process models with linearly parametrized intensity for application to earthquake data
Authors: Ogata Yosihiko , Katsura Koichi 
Published: July 2016

It is demonstrated that linear parametrization of the conditional intensity provides systematic classes of flexible models which are reasonably useful for calculating maximum likelihoods. To exemplify the modelling, seismic activity around Canberra is decomposed into components of evolutionary trend, clustering and periodicity. The causal relationship between earthquake sequences from two seismic regions is also analysed for a certain Japanese earthquake data set.
Some technical aspects of the modelling and calculations are described.