bluuebunny/crossref_metadata_2025 huggingface dataset:
On the expected number of crossings of a level in certain stochastic processes
Authors: Roes P. B. M.
Published: July 2016

We consider a stochastic process which increases and decreases by simple jumps as well as smoothly. The rate of smooth increase and decrease with time is a function of the state of the process. The process is not constant in time except when in the zero state. For such processes a relation is derived between the expected number of true crossings (as opposed to skippings by which we mean vertical crossings due to jumps) of a level x, say, and the time dependent distribution of the process. This result is applied to the virtual waiting time process of the GI/G/1 queue, where it is of particular interest when the zero level is considered, as the underlying crossing process is then a renewal process. It leads to a new derivation of the busy period distribution for this system. This serves as an example for the last brief section, where an indication is given as to how this method may be applied to the GI/G/s queue. Naturally, the present method is most powerful when the original process is a Markov process, so that renewal processes are imbedded at all levels. For an application to the M/G/1 queue, see Roes [3].
On a characterization property of finite irreducible Markov chains
Authors: Basawa I. V.
Published: July 2016

Let {Xk
}, k = 1, 2, ··· be a sequence of random variables forming a homogeneous Markov chain on a finite state-space, S = {1, 2, ···, s}. Xk
could be thought of as the state at time k of some physical system for which

are the (one-step) transition probabilities. It is assumed that all the states are inter-communicating, so that the transition matrix P = ((pij
)) is irreducible.
On random n-fold coincidences
Authors: Ivkovic Z. , Kocher M. , Stanojevic C. V.
Published: July 2016

The problem of random n-fold coincidences for Geiger counters was considered by Janossy [1] and Schrödinger [2]. In this note we consider a more general problem related to the following model.
Some central limit analogues for supercritical Galton-Watson processes
Authors: Heyde C. C.
Published: July 2016

It is possible to interpret the classical central limit theorem for sums of independent random variables as a convergence rate result for the law of large numbers. For example, ifXi, i= 1, 2, 3, ··· are independent and identically distributed random variables withEXi=μ, varXi= σ2< ∞ andthen the central limit theorem can be written in the formThis provides information on the rate of convergence in the strong lawas. (“a.s.” denotes almost sure convergence.) It is our object in this paper to discuss analogues for the super-critical Galton-Watson process.
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.
Generating functions for a class of one-dimensional random walks
Authors: Percus Ora Engelberg , Percus Jerome K.
Published: July 2016

A weighted Markov chain technique is used to find the generating functions for several restricted one-dimensional random walks. Examples with simple restrictions concern the number of penetrations of a penetrable barrier. Examples with compound restrictions include the number of full crossings of the origin. A typical asymptotic evaluation is carried out.
The definition of a multi-dimensional generalization of shot noise
Authors: Daley D. J.
Published: July 2016

The paper studies the formally defined stochastic process

where {tj
} is a homogeneous Poisson process in Euclidean n-space En
and the a.e. finite Em
-valued function f(·) satisfies |f(t)| = g(t) (all |t | = t), g(t) ↓ 0 for all sufficiently large t → ∞, and with either m = 1, or m = n and f(t)/g(t) =t/t. The convergence of the sum at (*) is shown to depend on

(i)

(ii)

(iii)

. Specifically, finiteness of (i) for sufficiently large X implies absolute convergence of (*) almost surely (a.s.); finiteness of (ii) and (iii) implies a.s. convergence of the Cauchy principal value of (*) with the limit of this principal value having a probability distribution independent of t when the limit in (iii) is zero; the finiteness of (ii) alone suffices for the existence of this limiting principal value at t = 0.
Tail equivalence and its applications
Authors: Resnick Sidney I.
Published: July 2016

If for two c.d.f.'s F(·) and G(·), 1 – F(x)/1 – G(x) → A, 0 <A <∞
, as x → ∞, then for normalizing constants an
> 0, bn, n > 1, Fn
(anx + bn
) → φ(x), φ(x) non-degenerate, iff Gn
(anx + bn
)→ φ A−1(x). Conversely, if Fn
(anx+bn
)→ φ(x), Gn
(anx + bn
) → φ'(x), φ(x) and φ'(x) non-degenerate, then there exist constants C >0 and D such that φ'(x) =φ(Cx + D) and limx→∞ 1 — F(x)/1 — G(x) exists and is expressed in terms of C and D, depending on which type of extreme value distribution φ(x) is. These results are used to study domain of attraction questions for products of distribution functions and to reduce the limit law problem for maxima of a sequence of random variables defined on a Markov chain (M.C.) to the independent, identically distributed (i.i.d.) case.
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

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)).
Corrections to “linear-intercept distributions do not characterize plane sets”
Authors: Mallows C. L. , Clark J. M. C.
Published: July 2016

Dr. J. Alan Steppe has kindly pointed out two serious flaws, and some others less serious, in the proof of our paper [2]. However these can all be corrected, so that the result remains valid.
Comparison of two replacement policies
Authors: Lešanovský Antonín
Published: July 2016

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.
An application of the system-point method to inventory models under continuous review
Authors: Azoury K. , Brill P. H.
Published: July 2016

This paper derives the stationary probability distribution of inventory level for continuous-review models, by means of the system-point method of level-crossing analysis. We analyze inventory problems with decaying products under (nQ, r) and (s, S) ordering policies and zero lead-time, and derive the relevant cost functions. Our results have implications for the case of positive lead-time and to a non-decaying inventory problem with two types of demand processes.
Exponential martingales and Wald's formulas for two-queue networks
Authors: Baccelli François
Published: July 2016

An exponential martingale is defined for a class of random walks in the positive quarter lattice which are associated with a wide variety of Markovian two-queue networks. Balance formulas generalizing Wald's exponential identity are derived from the regularity of several types of hitting times with respect to this martingale. In a queuing context, these formulas can be interpreted as functional relations of practical interest between the number of customers at certain epochs and the utilization of the queues up to these epochs.
On the asymptotic properties of a supercritical bisexual branching process
Authors: Bagley J. H.
Published: July 2016

An almost sure convergence result for the normed population size of a bisexual population model is proved. Properties of the limit random variable are deduced. The derivation of similar results for a general class of such processes is discussed.
On the moments of vacancy of random arcs on the circle
Authors: Henze Norbert
Published: July 2016

Place n arcs of equal length uniformly at random on the circumference of a circle. We give a simple probabilistic derivation of the moments of the uncovered portion of the circle.
Branching processes in near-critical random environments
Authors: Jagers Peter , Klebaner Fima
Published: July 2016

Branching processes are studied in random environments that are influenced by the population size and approach criticality as the population gets large. Results are applied to the polymerase chain reaction (PCR), which is empirically known to exhibit first exponential and then linear growth of molecule numbers.
Fitting the variance-gamma model to financial data
Authors: Seneta Eugene
Published: July 2016

This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.
On finite exponential moments for branching processes and busy periods for queues
Authors: Nakayama Marvin K. , Shahabuddin Perwez , Sigman Karl
Published: July 2016

Using a known fact that a Galton–Watson branching process can be represented as an embedded random walk, together with a result of Heyde (1964), we first derive finite exponential moment results for the total number of descendants of an individual. We use this basic and simple result to prove analogous results for the population size at time t and the total number of descendants by time t in an age-dependent branching process. This has applications in justifying the interchange of expectation and derivative operators in simulation-based derivative estimation for generalized semi-Markov processes. Next, using the result of Heyde (1964), we show that, in a stable GI/GI/1 queue, the length of a busy period and the number of customers served in a busy period have finite exponential moments if and only if the service time does.
Scoring probability forecasts for point processes: the entropy score and information gain
Authors: Daley Daryl J. , Vere-Jones David
Published: July 2016

Theentropy scoreof an observed outcome that has been given a probability forecastpis defined to be –logp.Ifpis derived from a probability model and there is a background model for which the same outcome has probabilityπ, then the log ratio log(p/π) is theprobability gain, and its expected value theinformation gain, for that outcome. Such concepts are closely related to the likelihood of the model and its entropy rate. The relationships between these concepts are explored in the case that the outcomes in question are the occurrence or nonoccurrence of events in a stochastic point process. It is shown that, in such a context, the mean information gain per unit time, based on forecasts made at arbitrary discrete time intervals, is bounded above by the entropy rate of the point process. Two examples illustrate how the information gain may be related to realizations with a range of values of ‘predictability'.
The eigenvalues of the empirical transition matrix of a Markov chain
Authors: Pritchard Geoffrey , Scott David J.
Published: July 2016

This paper investigates the probabilistic behaviour of the eigenvalue of the empirical transition matrix of a Markov chain which is of largest modulus other than 1, loosely called the second-largest eigenvalue. A central limit theorem is obtained for nonmultiple eigenvalues of the empirical transition matrix. When the Markov chain is actually a sequence of independent observations the distribution of the second-largest eigenvalue is determined and a test for independence is developed. The independence case is considered in more detail when the Markov chain has only two states, and some applications are given.
An inducing construction of quantum codes from classical error correcting codes
Authors: Parthasarathy K. R.
Published: July 2016

The aim of the present paper is to construct error correcting quantum codes from classical error correcting group codes by using the Schur orthogonality relations for characters of a finite abelian group and the Knill–Laflamme criterion for a quantum code to correct a pre-assigned family of errors. This is an abstraction and generalization of Shor's example of a nine qubit single error correcting quantum code.
Characterization by orthogonal polynomial systems of finite Markov chains
Authors: Seneta E.
Published: July 2016

The paper characterizes matriceswhich have a given system of vectors orthogonal with respect to a given probability distribution as its right eigenvectors. Results of Hoare and Rahman are unified in this context, then all matrices with a given orthogonal polynomial system as right eigenvectors under the constrainta0j= 0 forj≥ 2 are specified. The only stochastic matricesP ={pij} satisfyingp00+p01= 1 with the Hahn polynomials as right eigenvectors have the form of the Moran mutation model.
Misspecified change-point estimation problem for a Poisson process
Authors: Dabye Ali S. , Kutoyants Yury A.
Published: July 2016

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗
to an upper function h∗
at some unknown point θ
∗. What is known are continuous bounding functions g and h such that g∗
(t) ≤ g(t) ≤ h(t) ≤ h∗
(t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ
∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗
and h
∗.
Point process modelling of reservoir-induced seismicity
Authors: Imoto Masajiro
Published: July 2016

A point process procedure can be used to study reservoir-induced seismicity (RIS), in which the intensity function representing earthquake hazard is a combination of three terms: a constant background term, an ETAS (epidemic-type aftershock sequence) term for aftershocks, and a time function derived from observation of water levels of a reservoir. This paper presents the results of such a study of the seismicity in the vicinity of the Tarbela reservoir in Pakistan. Making allowance for changes in detection capability and the background seismicity related to tectonic activity, earthquakes of magnitude ≥ 2.0, occurring between May 1978 and January 1982 and whose epicentres were within 100 km of the reservoir, were used in this analysis. Several different intensities were compared via their Akaike information criterion (AIC) values relative to those of a Poisson process. The results demonstrate that the seismicity within 20 km of the reservoir correlates with water levels of the reservoir, namely, active periods occur about 250 days after the appearance of low water levels. This suggests that unloading the reservoir activates the seismicity beneath it. Seasonal variations of the seismicity in an area up to 100 km from the reservoir were also found, but these could not be adequately interpreted by an appropriate RIS mechanism.
On the structure of proper Black-Scholes formulae
Authors: Whittle Peter
Published: July 2016

The thinking behind the original Black-Scholes formula is criticised on the grounds that it holds out the quite unrealistic prospect of risk-free operation, that it can sacrifice asset maximisation to exact meeting of the contract, and that it restricts investment to those stocks on which an option is being sold. An alternative approach is given, based on a model of risk-averse asset maximisation, which, while meeting these criticisms, gives the option price in the familiar form of a discounted and weighted conditional expectation of the seller's liability at maturity. This evaluation is extended to a completely general stochastic model of stock price evolution; consideration is also given to the possibility of seller's ruin.
Estimating interannual variability arising from weather events
Authors: Zheng Xiaogu , Renwick James
Published: July 2016

The advantages and limitations of frequency domain and time domain methods for estimating the interannual variability arising from day-to-day weather events are summarized. A modification of the time domain method is developed and its application in examining a precondition for the frequency domain method is demonstrated. A combined estimation procedure is proposed: it takes advantage of the strengths of both methods. The estimation procedures are tested with sets of synthetic data and are applied to long time series of three meteorological parameters. The impacts of the different methods on tests of potential long-range predictability for seasonal means are also discussed.
An extension of a lemma of Wald
Authors: Robbins H. , Samuel E.
Published: July 2016

We define a natural extension of the concept of expectation of a random variable y as follows: M(y) = a if there exists a constant − ∞ ≦ a ≦ ∞ such that if y
1, y
2, … is a sequence of independent identically distributed (i.i.d.) random variables with the common distribution of y then
On the model of Weiss for the spread of epidemics by carriers
Authors: Dietz Klaus
Published: July 2016

1. Recently Weiss [7] constructed a stochastic model for the spread of diseases e.g. typhoid, by carriers. He assumed that a carrier is eliminated in (t, t + dt) with probability βrdt, where r is the number of carriers extant at time t and that a susceptible is infected in (t, t + dt) with probability arsdt where s is the number of susceptibles at time t. Thus only the carriers are responsible for the spread of the disease.
Extreme nth moments for distributions on [0, 1] and the inverse of a moment space map
Authors: Skibinsky Morris
Published: July 2016

Let n be a positive integer. Denote by Mn
the convex, closed, bounded, and n-dimensional set of all n-tuples (c
1, c
2,···, c
n) such that

for some probability measure a on the Borel subsets of the unit interval I = [0,1].
Products of distribution functions attracted to extreme value laws
Authors: Resnick Sidney I.
Published: July 2016

When is the product of the d.f.'s H
1(·), ···, Hm
(·) attracted to an extreme value law φ(x)? We associate with each Hi
(·) its A-function

Hi
(x) is attracted to φ(x) if each Hi
(x) is in the domain of attraction of φ(x) and Ai
(z) ~ Aj
(z), 1 ≦ i, j ≦ m. Equivalence of A-functions determines an equivalence relation which partitions the domain of attraction of φ(x)into one or more convex sets. These sets fail to be closed under passages to the limit (complete convergence).
Mixing properties of harris chains and autoregressive processes
Authors: Athreya Krishna B. , Pantula Sastry G.
Published: July 2016

Let {Yn:n≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distributionπ(·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.
Tangential measure on the set of convex infinite cylinders
Authors: Molter Ursula Maria
Published: July 2016

We find a ‘natural' measure on the set of convex infinite cylinders touching a convex bodyKinEn.Using the curvature measures, we can calculate the probability that a convex infinite cylinder and a convex bodyKare tangent in some previously determined regions. As a particular case we obtain a measure on allq-planes touchingK.
An optimal inspection and replacement policy for a deteriorating system
Authors: Ohnishi Masamitsu , Kawai Hajime , Mine Hisashi
Published: July 2016

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.
Modeling the effect of erosion on crop production
Authors: Todorovic P. , Gani J.
Published: July 2016

This paper is concerned with a model for the effect of erosion on crop production. Crop yield in the year n is given by X(n) = YnLn, where is a sequence of strictly positive i.i.d. random variables such that E{Y
1} <∞, and is a Markov chain with stationary transition probabilities, independent of . When suitably normalized, leads to a martingale which converges to 0 almost everywhere (a.e.) as n → ∞. In addition, for large n, the distribution of Ln
is approximately lognormal. The conditional expectations and probabilities of , given the past history of the process, are determined. Finally, the asymptotic behaviour of the total crop yield is discussed. It is established that under certain regularity conditions Sn
converges a.e. to a finite-valued random variable S whose Laplace transform can be obtained as the solution of a Volterra-type linear integral equation.
On the number of leaves of a euclidean minimal spanning tree
Authors: Steele J. Michael , Shepp Lawrence A. , Eddy William F.
Published: July 2016

Let Vk,n
be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi
, , where the Xi
are independent, absolutely continuous random variables with values in Rd. It is proved that n
–1
Vk,n
converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.
Characterization of the logistic and loglogistic distributions by extreme value related stability with random sample size
Authors: Voorn W. J.
Published: July 2016

Maximum stability of a distribution with respect to a positive integer random variable N is defined by the property that the type of distribution is not changed when considering the maximum value of N independent observations. The logistic distribution is proved to be the only symmetric distribution which is maximum stable with respect to each member of a sequence of positive integer random variables assuming value 1 with probability tending to 1. If a distribution is maximum stable with respect to such a sequence and minimum stable with respect to another, then it must be logistic, loglogistic or ‘backward' loglogistic. The only possible sample size distributions in these cases are geometric.
Saddlepoint expansions for conditional distributions
Authors: Skovgaard Ib M.
Published: July 2016

A saddlepoint expansion is given for conditional probabilities of the form where is an average of n independent bivariate random vectors. A more general version, corresponding to the conditioning on a p – 1-dimensional linear function of a p-dimensional variable is also included. A separate formula is given for the lattice case. The expansion is a generalization of the Lugannani and Rice (1980) formula, which reappears if and are independent. As an example an approximation to the hypergeometric distribution is derived.
Quasi-stationary distributions and one-dimensional circuit-switched networks
Authors: Ziedins Ilze
Published: July 2016

We discuss the quasi-stationary distribution obtained when a simple birth and death process is conditioned on never exceeding K. An application of this model to one-dimensional circuit-switched communication networks is described, and some special cases examined.
Inequalities for the M/G/∞ queue and related shot noise processes
Authors: Huffer Fred W.
Published: July 2016

Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.
Server sharing with a limited number of service positions and symmetric queues
Authors: Avi-Itzhak Benjamin , Halfin Shlomo
Published: July 2016

A class of M/G/1 time-sharing queues with a finite number of service positions and unlimited waiting space is described. The equilibrium distribution of symmetric queues belonging to this class is invariant under arbitrary service-independent reordering of the customers at instants of arrivals and departures. The delay time distribution, in the special case of one service position where preempted customers join the end of the line, is provided in terms of Laplace transforms and generating functions. It is shown that placing preempted customers at the end of the line rather than at the beginning of the line results in a reduction of the delay time variance. Comparisons with the delay time variance of the case of unlimited number of service positions (processor sharing system) are presented.
On almost sure convergence of an erosion process due to Todorovic and Gani
Authors: Puri Prem S.
Published: July 2016

The questions of almost sure convergence of the sequence Xn
defined below in (1) as well as that of to a finite limit are settled here. These sequences arise in a simple stochastic model for crop erosion considered by Todorovic and Gani (1987).
Non-singularity and asymptotic independence
Authors: Bloomfield Peter
Published: July 2016

A stationary stochastic process must satisfy various requirements to make it a realistic model for a phenomenon in the real world. Some of these requirements are quantitative, such as agreement of distribution or moments. Other, more qualitative requirements deal with the general behavior of the process. Two such requirements are non-singularity and asymptotic independence. Each will be discussed from a variety of points of view, and given precise definition in a succession of progressively stronger forms.
Order estimation by accumulated prediction errors
Authors: Rissanen Jorma
Published: July 2016

This paper presents a new criterion based on prediction error which allows the estimation of the number of parameters as well as structures in statistical models. The criterion is valid for short and long samples alike. Unlike Akaike's earlier criterion, also based on prediction error, the criterion proposed here appears to produce consistent error estimates in ARMA processes.
The ‘derived’ moving-average model and its role in causality
Authors: Penm J. H. W. , Terrell R. D.
Published: July 2016

In the situations where restrictions on the multivariate subset AR model are known, we propose methods of providing suitable standard errors of estimate and prediction which assist in assessing the importance of the coefficients appearing the ‘derived' moving-average (MA) model. The coefficient patterns of the derived moving-average model are proposed as an alternative basis for detecting Granger-causality.
On a model for a time series of cross-sections
Authors: Robinson P. M.
Published: July 2016

Dynamic stationary models for mixed time series and cross-section data are studied. The models are of simple, standard form except that the unknown coefficients are not assumed constant over the cross-section; instead, each cross-sectional unit draws a parameter set from an infinite population. The models are framed in continuous time, which facilitates the handling of irregularly-spaced series, and observation times that vary over the cross-section, and covers also standard cases in which observations at the same regularly-spaced times are available for each unit. A variety of issues are considered, in particular stationarity and distributional questions, inference about the parameter distributions, and the behaviour of cross-sectionally aggregated data.
The comparison of transient responses to stimuli
Authors: Cameron Murray A.
Published: July 2016

In some experiments an ‘observation' is a time series and the ‘treatments' are stimuli which elicit changes in the nature of the time series for only a short period. One approach to analysing data from such experiments is presented here. Tests are given for detecting responses in such experiments, and for comparing responses elicited under different treatment regimes. The tests are based on frequency-domain estimates of the prediction variance for stationary time series. If several stimuli are applied within each observed time series at regular intervals, then the method of analysis may be designed so that the estimates of the different responses are orthogonal and most of the calculations can be performed using standard analysis of variance programs.
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.
A simultaneous test in the presence of nested alternative hypotheses
Authors: Hosoya Yuzo
Published: July 2016

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.
Asymptotic expansions for time series statistics
Authors: Tanaka Katsuto
Published: July 2016

Asymptotic expansions for the distributions of estimators and test statistics are derived in connection with time series models. The expansions relate to marginal and joint distributions together with the percentiles of marginal distributions. We also consider transforming a statistic so that the transformed statistic has a distribution that coincides with its asymptotic distribution up to a higher order.
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.
Mixed Cox processes, with an application to accident statistics
Authors: Bartlett M. S.
Published: July 2016

A doubly stochastic switching model previously used by the author to check against doubly stochastic ‘white-noise' models is generalized in the case of Poisson processes to any distribution of fluctuating intensity rates. The resulting Cox process is used in place of a simple Poisson process as the basis of a mixed model, which is then fitted to some data on automobile accidents previously analysed by Seal (1980) in terms of a mixed Poisson process. It is shown that there is just significant evidence in favour of some additional heterogeneity ‘within' each year for individual drivers; the nature of the data analysed (yearly time intervals) does not, however, allow discrimination between heterogeneity which is definitely attributable to a common fluctuating environment, and that which is in effect independent for each driver.
On the equivalence of two stochastic approaches to spline smoothing
Authors: Ansley Craig F. , Kohn Robert
Published: July 2016

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.
The non-homogeneous Markov system in a stochastic environment
Authors: Tsantas N. , Vassiliou P.-C. G.
Published: July 2016

We introduce and define for the first time the concept of a non-homogeneous Markov system in a stochastic environment (S-NHMS). The problem of finding the expected population structure in an S-NHMS is studied, and important properties among the basic parameters of the S-NHMS are established. Moreover, we study the problem of maintaining the relative sizes of the states in a stochastic environment applying control in the input process. Among other things, we provide the probability of maintaining any vector of relative state sizes. Also strategies for attaining in an optimal way a desired relative structure are designed, with the use of a given algorithm. Finally, an illustration is provided of the present results in a manpower system.
Analysis of an M/G/1/K/N queue
Authors: Takine T. , Takagi H. , Hasegawa T.
Published: July 2016

A steady-state analysis of an M/G/1 queue with a finite capacity (K) and a finite population (N) of customers is given. The queue size distribution in this M/G/1/K/N system can be derived from the known queue size distribution in the corresponding M/G/1//N system. The system throughput, the mean response time, and the blocking probability are then calculated. The joint distributions of the queue size and the remaining service times are used to obtain the distributions of the unfinished work in the service facility and the waiting time of an accepted customer.
A new look at the Moran dam
Authors: Stadje W.
Published: July 2016

For the original Moran dam with independent and identically distributed inputs a representation of the stationary distribution is given which readily provides a geometric rate of convergence to this distribution. For the integer-valued case the stationary distribution can be expressed in terms of simple boundary crossing probabilities for the underlying random walk.
On Some Ageing Properties of General Repair Processes
Authors: Finkelstein Maxim
Published: July 2016

We consider ageing properties of a general repair process. Under certain assumptions we prove that the expectation of an age at the beginning of the next cycle in this process is smaller than the initial age of the previous cycle. Using this reasoning, we show that the sequence of random ages at the start (end) of consecutive cycles is stochastically increasing and is converging to a limiting distribution. We discuss possible applications and interpretations of our results.
Markov Additive Processes and Repeats in Sequences
Authors: Spouge John L.
Published: July 2016

Computer analysis of biological sequences often detects deviations from a random model. In the usual model, sequence letters are chosen independently, according to some fixed distribution over the relevant alphabet. Real biological sequences often contain simple repeats, however, which can be broadly characterized as multiple contiguous copies (usually inexact) of a specific word. This paper quantifies inexact simple repeats as local sums in a Markov additive process (MAP). The maximum of the local sums has an asymptotic distribution with two parameters (λ and k), which are given by general MAP formulas. The general MAP formulas are usually computationally intractable, but an essential simplification in the case of repeats permits λ and k to be computed from matrices whose dimension equals the size of the relevant alphabet. The simplification applies to some MAPs where the summand distributions do not depend on consecutive pairs of Markov states as usual, but on pairs with a fixed time-lag larger than one.
Explicit Gittins Indices for a Class of Superdiffusive Processes
Authors: Filliger Roger , Hongler Max-Olivier
Published: July 2016

We explicitly calculate the dynamic allocation indices (i.e. the Gittins indices) for multi-armed Bandit processes driven by superdiffusive noise sources. This class of model generalizes former results derived by Karatzas for diffusive processes. In particular, the Gittins indices do, in this soluble class of superdiffusive models, explicitly depend on the noise state.
On the subcritical Bellman-Harris process with immigration
Authors: Pakes A. G. , Kaplan Norman
Published: July 2016

Some necessary and sufficient conditions are found for the existence of a proper non-degenerate limiting distribution for a Bellman-Harris age-dependent branching process with a compound renewal immigration component. A number of these results are applicable to the batch arrival GI/G/∞ queueing process. Some aspects of the situation when there is no such limiting distribution are considered. The situation when the immigration component is a nonhomogeneous compound Poisson process is briefly considered.
The number of departures from a semi-Markov queue
Authors: McNickle D. C.
Published: July 2016

In this note an identity due to Arjas (1972) is used to express the distribution of the number of departures from a single server queue in which both service and interarrival times may depend on customer type in terms of the busy period and busy cycle processes.
The estimation of frequency
Authors: Hannan E. J.
Published: July 2016

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequencyθ0, is in fact 0 or <it is shown that the estimate,, satisfiesforN≧N0(ω) whereN0(ω) is an integer, determined by the realisation,ω, of the process, that is almost surely finite.
The asymptotic frequencies of the types in a multitype age-dependent branching process allowing immigration
Authors: Radcliffe J.
Published: July 2016

The mean square and almost sure convergence of W(t) = e–αt

Z(t) is proved for a super-critical multitype age-dependent branching process allowing immigration at the epochs of a renewal process. It is shown that the Malthusian parameter, asymptotic frequencies of types and stationary age distributions are the same for the processes with and without immigration.
RUMOURS, RIOTS AND THE REJECTION OF MASS DRUG ADMINISTRATION FOR THE TREATMENT OF SCHISTOSOMIASIS IN MOROGORO, TANZANIA
Authors: Hastings Julie
Published: July 2016

In 2008 in Morogoro region, Tanzania, mass drug administration (MDA) to school-aged children to treat two neglected tropical diseases (NTDs) – urinary schistosomiasis and soil-transmitted helminths – was suspended by the Ministry of Health and Social Welfare after riots broke out in schools where drugs were being administered. This article discusses why this biomedical intervention was so vehemently rejected, including an eyewitness account. As the protest spread to the village where I was conducting fieldwork, villagers accused me of bringing medicine into the village with which to ‘poison’ the children and it was necessary for me to leave immediately under the protection of the Tanzanian police. The article examines the considerable differences between biomedical and local understandings of one of these diseases, urinary schistosomiasis. Such a disjuncture was fuelled further by the apparent rapidity of rolling out MDA and subsequent failures in communication between programme staff and local people. Rumours of child fatalities as well as children’s fainting episodes and illnesses following treatment brought about considerable conjecture both locally and nationally that the drugs had been either faulty, counterfeit, hitherto untested on humans or part of a covert sterilization campaign. The compelling arguments by advocates of MDA for the treatment of NTDs rest on the assumption that people suffering from these diseases will be willing to swallow the medicine. However, as this article documents, this is not always the case. For treatment of NTDs to be successful it is not enough for programmes to focus on economic and biomedical aspects of treatment, rolling out ‘one size fits all’ programmes in resource-poor settings. It is imperative to develop a biosocial approach: to consider the local social, biological, historical, economic and political contexts in which these programmes are taking place and in which the intended recipients of treatment live their lives. If this is not done, the world’s poor will continue to be neglected.
Microstructure in two- and three-dimensional hybrid simulations of perpendicular collisionless shocks
Authors: Burgess David , Hellinger Petr , Gingell Imogen , Trávníček Pavel M.
Published: July 2016

Supercritical collisionless perpendicular shocks have an average macrostructure determined primarily by the dynamics of ions specularly reflected at the magnetic ramp. Within the overall macrostructure, instabilities, both linear and nonlinear, generate fluctuations and microstructure. To identify the sources of such microstructure, high-resolution two- and three-dimensional simulations have been carried out using the hybrid method, wherein the ions are treated as particles and the electron response is modelled as a massless fluid. We confirm the results of earlier two-dimensional (2-D) simulations showing both field-parallel aligned propagating fluctuations and fluctuations carried by the reflected-gyrating ions. In addition, it is shown that, for 2-D simulations of the shock coplanarity plane, the presence of short-wavelength fluctuations in all magnetic components is associated with the ion Weibel instability driven at the upstream edge of the foot by the reflected-gyrating ions. In 3-D simulations we show for the first time that the dominant microstructure is due to a coupling between field-parallel propagating fluctuations in the ramp and the motion of the reflected ions. This results in a pattern of fluctuations counter-propagating across the surface of the shock at an angle inclined to the magnetic field direction, due to a combination of field-parallel motion at the Alfvén speed of the ramp and motion in the sense of gyration of the reflected ions.
The nature of music itself, and the knowledge versus skills debate in music education
Authors: FAUTLEY MARTIN , MURPHY REGINA
Published: July 2016

Back in 2013, in the BJME editorial for issue 30(2), we considered the place of knowledge in the curriculum (Fautley & Murphy, 2013). Things have not stood still since that date, certainly in England, and other parts of the world too. What we have now is a situation where the idea of knowledge as assuming supremacy over skills is on the increase. For those of us concerned with music education, many aspects of this increasingly fractious debate are to be viewed with concern. Allied to this, we have neoliberal-leaning governments in many parts of the world, Britain included, who seem to find it difficult to understand the important role that music education has – or should have – in the education of our children and young people. Indeed, in the UK, the education secretary is on record as making this observation:

Education secretary Nicky Morgan has warned young people that choosing to study arts subjects at school could ‘hold them back for the rest of their lives’ (The Stage, 2014)

This attitude, and Britain is certainly not alone in this, is clearly going to be problematic for those of us involved in music and the arts.
Prosodic differences between declaratives and interrogatives in infant-directed speech
Authors: GEFFEN SUSAN , MINTZ TOBEN H.
Published: July 2016

In many languages, declaratives and interrogatives differ in word order properties, and in syntactic organization more broadly. Thus, in order to learn the distinct syntactic properties of the two sentence types, learners must first be able to distinguish them using non-syntactic information. Prosodic information is often assumed to be a useful basis for this type of discrimination, although no systematic studies of the prosodic cues available to infants have been reported. Analysis of maternal speech in three Standard American English-speaking mother–infant dyads found that polar interrogatives differed from declaratives on the patterning of pitch and duration on the final two syllables, butwh-questions did not. Thus, while prosody is unlikely to aid discrimination of declaratives fromwh-questions, infant-directed speech provides prosodic information that infants could use to distinguish declaratives and polar interrogatives. We discuss how learners could leverage this information to identify all question forms, in the context of syntax acquisition.