bluuebunny/crossref_metadata_2025 huggingface dataset:
On the distribution and moments of the strength of a bundle of filaments
Authors: Suh M. W. , Bhattacharyya B. B. , Grandage A.
Published: July 2016

Small sample and large sample properties of the bundle strength of parallel filaments studied earlier by Daniels (1945) and Sen, Bhattacharyya, Suh (1969) have been developed here by probabilistic argument. The statistics belong to a family or class of statistics, each of which forms a reverse semi-martingale sequence. Certain moment properties are also discussed.
On sums of random variables defined on a two-state Markov chain
Authors: Helgert H. J.
Published: July 2016

Assume the sequence of random variables x
0, x
1, x
2, ··· forms a two-state, homogeneous Markov chain with transition probabilities

and initial probabilities
Identifiability in GI/G/k queues
Authors: Ross Sheldon M.
Published: July 2016

Consider a queueing system in which customers arrive in accordance with a renewal process having an interarrival distribution F, and in which the service times of customers are independent and have distribution G. Moreover, suppose that there are k (k ≦ ∞) servers and that an arriving customer is immediately served if he finds one of the servers free, and if not then he joins the queue.
Interval estimates of language divergence times
Authors: Dobson A. J.
Published: July 2016

It is often convenient to construct a branching diagram to represent the relationships between languages belonging to the same language family (for example, between Romance languages such as Rumanian, Italian, French and Spanish). It is desirable that the diagram should illustrate both the closeness of the relationships (that is, which pairs of languages have an immediate common ancestor and which are more remotely related) and the relative chronology of the languages. In this paper, the problem of estimating the time since two languages had a common ancestor and were the same is considered. Interval estimates are sought since, in general, consistent point estimates may be impossible; a numerical example is given to illustrate this.
Limit theorems for a general critical branching process
Authors: Durham Stephen D.
Published: July 2016

A general branching process begins with an initial object born at time 0. The initial object lives a random length of time and, during its life-time, has offspring which reproduce and die as independent probabilistic copies of the parent. Number and times of births to a parent are random and, once an object is born, its behavior is assumed to be independent of all other objects, independent of total population size and independent of absolute time. The life span of a parent and the number and times its offspring arrive may be interdependent. Multiple births are allowed. The process continues as long as there are objects alive.
Multitype branching processes in random environments
Authors: Weissner Edward W.
Published: July 2016

Consider the classical Galton-Watson process described by Harris ((1963), Chapter 1). Recently this model has been generalized in Smith (1968), Smith and Wilkinson (1969), and Wilkinson (1967). They removed the restrictive assumption that the particles always divide in accordance with the same p.g.f. Instead, they assumed that at each unit of time, Nature be allowed to choose a p.g.f. from a class of p.g.f.'s, independently of the population, past and present, and the previously selected p.g.f.'s, which would then be assigned to the present population. Each particle of the present population would then split, independently of the others, in accordance with the selected p.g.f. This process, called a branching process in a random environment (BPRE), is clearly more applicable than the Galton-Watson process. Moreover, Smith and Wilkinson have found necessary and sufficient conditions for almost certain extinction of the BPRE which are almost as easy to verify as those for the Galton-Watson process.
Branching processes with immigration
Authors: Pakes A. G.
Published: July 2016

Consider a branching process in which each individual reproduces independently of all others and has probability aj
(j = 0, 1, ···) of giving rise to j progeny in the following generation, and in which there is an independent immigration component where, with probability bj
(j = 0, 1, ···) j objects enter the population at each generation. Then letting Xn
(n = 0, 1, ···) be the population size of the nth generation, it is known (Heathcote (1965), (1966)) that {Xn
} defines a Markov chain on the non-negative integers and it is called a branching process with immigration (b.p.i.). We shall call the process sub-critical or super-critical according as the mean number of offspring of an individual, , satisfies α < 1 or α > 1, respectively. Unless stated specifically to the contrary, we assume that the following condition holds.
Expenditure patterns for risky R and D projects
Authors: Kamien Morton I. , Schwartz Nancy L.
Published: July 2016

In this paper we derive the time pattern of optimal planned expenditures for R and D projects in which the total effort required to complete the research satisfactorily is not known. Theorem 1 summarizes our results under alternative assumptions regarding the behavior of the function governing the supposed probability of completing the R and D satisfactorily with incremental effort. In addition, an easily employed necessary condition for the R and D project to be worthwhile is provided in Theorem 2.
Spectral inference over narrow bands
Authors: Hannan E. J. , Thomson P. J.
Published: July 2016

We consider a vector, discrete, time sequence x(n), n = 0, ± 1 ···, of p components Xj
(n), j = 1, ··· p. For the most part we shall assume x(n) to be strictly stationary and with finite variances. Thus if μ is the mean vector we shall have
Selective interaction of a poisson and renewal process: the dependency structure of the intervals between responses
Authors: Lawrance A. J.
Published: July 2016

This paper studies the dependency structure of the intervals between responses in the renewal inhibited Poisson process, and continues the author's earlier work on this type of process ((1970a), (1970b)). A new approach to the intervals between events in a stationary point process, based on the idea of an average event, is introduced. Average event initial conditions (as opposed to equilibrium initial conditions previously determined) for the renewal inhibited Poisson process are obtained and event stationarity of the resulting response process is established. The joint distribution and correlation between pairs of contiguous synchronous intervals is obtained; further, the joint distribution of non-contiguous pairs of synchronous intervals is derived. Finally, the joint distributions of pairs of contiguous synchronous and asynchronous intervals are related, and a similar but more general stationary point result is conjectured.
Notes on Natvig's measure of importance of system components
Authors: Norros Ilkka
Published: July 2016

Natvig's measure of importance of system components is defined and investigated, using martingale notions and methods. Most results are proved in the case of dependent component life lengths. The sum of the ‘absolute importances' of the components is studied as a quantity expressing the ‘share of failures' in the destruction of the system, contrasted to the ‘share of time’.
Optimal allocation of components in parallel–series and series–parallel systems
Authors: El-Neweihi Emad , Proschan Frank , Sethuraman Jayaram
Published: July 2016

This paper shows how majorization and Schur-convex functions can be used to solve the problem of optimal allocation of components to parallel-series and series-parallel systems to maximize the reliability of the system. For parallel-series systems the optimal allocation is completely described and depends only on the ordering of component reliabilities. For series-parallel systems, we describe a partial ordering among allocations that can lead to the optimal allocation. Finally, we describe how these problems can be cast as integer linear programming problems and thus the results obtained in this paper show that when some linear integer programming problems are recast in a different way and the techniques of Schur functions are used, complete solutions can be obtained in some instances and better insight in others.
A mosaic of triangular cells formed with sequential splitting rules
Authors: Cowan Richard
Published: July 2016

The iterative division of a triangle by chords which join a randomly-selected vertex of a triangle to the opposite side is investigated. Results on the limiting random graph which eventuates are given. Aspects studied are: the order of vertices; the fragmentation of chords; age distributions for elements of the graph; various topological characterisations of the triangles. Different sampling protocols are explored. Extensive use is made of the theory of branching processes.
Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence
Authors: Anh V. V. , Leonenko N. N. , Sakhno L. M.
Published: July 2016

This paper provides a quasi-likelihood or minimum-contrast-type method for the parameter estimation of random fields in the frequency domain based on higher-order information. The estimation technique uses the spectral density of the general kth order and allows for possible long-range dependence in the random fields. To avoid bias due to edge effects, data tapering is incorporated into the method. The suggested minimum contrast functional is linear with respect to the periodogram of kth order, hence kernel estimation for the spectral densities is not needed. Furthermore, discretization is not required in the estimation of continuously observed random fields. The consistency and asymptotic normality of the resulting estimators are established. Illustrative applications of the method to some problems in mathematical finance and signal detection are given.
Stieltjes classes for moment-indeterminate probability distributions
Authors: Stoyanov Jordan
Published: July 2016

LetFbe a probability distribution function with densityf. We assume that (a) F has finite moments of any integer positive order and (b) the classical problem of moments forFhas a nonunique solution (Fis M-indeterminate). Our goal is to describe a, wherehis a ‘small' perturbation function. Such a classSconsists of different distributionsFε(fεis the density ofFε) all sharing the same moments as those ofF, thus illustrating the nonuniqueness ofF, and of anyFε,in terms of the moments. Power transformations of distributions such as the normal, log-normal and exponential are considered and for them Stieltjes classes written explicitly. We define a characteristic ofScalled anindex of dissimilarityand calculate its value in some cases. A new Stieltjes class involving a power of the normal distribution is presented. An open question about the inverse Gaussian distribution is formulated. Related topics are briefly discussed.
The moment index of minima
Authors: Daley D. J.
Published: July 2016

For a random variable (RV) X its moment index κ(X) ≡ sup{κ : E(|X|
κ
) < ∞} lies in 0 ≤ κ (X) ≤∞; it is a critical quantity and finite for heavy-tailed RVs. The paper shows that κ (min(X, Y)) ≥ κ(X) + κ (Y) for independent non-negative RVs X and Y. For independent non-negative ‘excess' RVs Xs
and Ys
whose distributions are the integrated tails of X and Y, κ (X) + κ (Y) ≤ κ (min(Xs, Ys
)) + 2 ≤ κ (min(X, Y)). An example shows that the inequalities can be strict, though not if the tail of the distribution of either X or Y is a regularly varying function.
Geometric L
2 and
L
1 convergence are equivalent for reversible Markov chains
Authors: Roberts Gareth O. , Tweedie Richard L.
Published: July 2016

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.
An innovation approach to non-Gaussian time series analysis
Authors: Ozaki Tohru , Iino Mitsunori
Published: July 2016

The paper shows that the use of both types of random noise, white noise and Poisson noise, can be justified when using an innovations approach. The historical background for this is sketched, and then several methods of whitening dependent time series are outlined, including a mixture of Gaussian white noise and a compound Poisson process: this appears as a natural extension of the Gaussian white noise model for the prediction errors of a non-Gaussian time series. A statistical method for the identification of non-linear time series models with noise made up of a mixture of Gaussian white noise and a compound Poisson noise is presented. The method is applied to financial time series data (dollar-yen exchange rate data), and illustrated via six models.
Estimation of the upper cutoff parameter for the tapered Pareto distribution
Authors: Kagan Y. Y. , Schoenberg F.
Published: July 2016

The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.
Exploratory analysis of earthquake clusters by likelihood-based trigger models
Authors: Ogata Yosihiko
Published: July 2016

The paper considers the superposition of modified Omori functions as a conditional intensity function for a point process model used in the exploratory analysis of earthquake clusters. For the examples discussed, the maximum likelihood estimates converge well starting from appropriate initial values even though the number of parameters estimated can be large (though never larger than the number of observations). Three datasets are subjected to different analyses, showing the use of the model to discover and study individual clustering features.
A mathematical study of the founder principle of evolutionary genetics
Authors: Holgate P.
Published: July 2016

Some comparisons are made between various characteristics of the genetic structures of populations of the same size and age, which have (i) evolved from a small founder population, and (ii) evolved from a population which has been of constant size throughout the period considered.
A Combinatorial method for a class of matrix games
Authors: Restrepo Rodrigo A.
Published: July 2016

The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.
The expected number and angle of intersections between random curves in a plane
Authors: Morton R.R.A.
Published: July 2016

Consider a plane containing a set of curves. Suppose a separate set of curves is constrained to lie at random on a particular region of this plane. In this note an expression is obtained for the expected number of intersections between the two sets of curves, and it is shown that the angles between the two sets at their points of intersection are distributed as ½ sin θ.
Equilibrium behavior of population genetic models with non-random mating. Part II: Pedigrees, Homozygosity and Stochastic Models
Authors: Karlin Samuel
Published: July 2016

Wright (1921) computed various correlations of relatives by a rather cumbersome procedure called the “method of path coefficients”. Wright's method is basically a disguised form of the use of Bayes' rule and the law of total probabilities. Malecot (1948) reorganized Wright's calculations by introducing the fundamental concept of identity by descent and exploiting its properties. The method of identity by descent has been perfected and developed by Malécot and his students, especially Gillois, Jauquard and Bouffette. Kempthorne (1957) has applied the concept of identity by descent to the study of quantitative inheritance. Kimura (1963) elegantly employed the ideas of identity by descent in determining rates of approach to homozygosity in certain mating situations with finite population size. Later in this chapter we will extend and refine the results of Kimura (1963) to give a more complete study of rates of approach to homozygosity. Ellison (1966) established several important limit theorems corresponding to polyploid, multi-locus random mating infinite populations by judicious enlargement of the concepts of identity by descent. Kesten (unpublished)) has recently refined the technique of Ellison.
On an extension of Gani's model for attachment of phages to bacteria
Authors: Bhat B. R.
Published: July 2016

In recent papers Yassky (1962) and Gani (1965) have considered respectively deterministic and stochastic models for the attachment of phages to bacteria. Following Brenner's (1965) conjecture they assumed that there is a maximum, S (say), to the number of phages that can be attached to a bacterium. In this note, Gani's (1965) results will be obtained starting from a different set of assumptions. This modification enables us to consider the case when S is a random variable, which probably is a more realistic assumption. Some remarks on the problem of estimation for the latter model are given in Section 3.
Queues with time-dependent arrival rates. II — The maximum queue and the return to equilibrium
Authors: Newell G. F.
Published: July 2016

During a rush hour, the arrival rateλ(t) of customers to a service facility is assumed to increase to a maximum value exceeding the service rateμ, and then decrease again. In Part I it was shown that, afterλ(t) has passedμ, the expected queueE{X(t)} exceeds that given by the deterministic theory by a fixed amount, (0.95)L, which is proportional to the (–1/3) power ofa(t) =dλ(t)/dtevaluated at timet= 0 whenλ(t) =μ.The maximum ofE{X(t)}, therefore, occurs whenλ(t) again is equal toμat timet1as predicted by deterministic queueing theory, but is larger than given by the deterministic theory by this same constant (0.95)L(providedt1is sufficiently large). It is shown here that the maximum queue, suptX(t) is, approximately normally distributed with a mean (0.95) (L+L1) larger than predicted by deterministic theory whereL, is proportional to the (–1/3) power ofa(t1). We also investigate the distribution ofX(t) at the end of the rush hour when the queue distribution returns to equilibrium. During the transition, the queue distribution is approximately a mixture of a truncated normal and the equilibrium distributions. These results are applied to a case whereλ(t) is quadratic int.
A stochastic process whose successive intervals between events form a first order Markov chain — I
Authors: Lampard D. G.
Published: July 2016

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind.

Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.
A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows
Authors: Lloyd Emlyn H.
Published: July 2016

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).
Recurrence for Markov processes on N lines
Authors: Pinsky Mark
Published: July 2016

Let Λ = R
1 × {1, 2, ···, N} denote N copies of the real line and ξ(t) = (X(t), α(t))be a right-continuous Markov process taking values in A having transition function of the form P(t, (x, α), A × {β}) = Fαβ
(t, A – x). Fukushima and Hitsuda [2] have found the most general such transition function; the (matrix) logarithm of its characteristic function is decomposed into a Lévy-Khintchine integral on the diagonal and multiples of characteristic functions off the diagonal.
On extreme stable laws and some applications
Authors: Eaton Morris L. , Morris Carl , Rubin Herman
Published: July 2016

It is shown that the extreme stable laws have one-sided moment generating functions with interesting mathematical forms. The fact that one of these forms, zcz
, is a moment generating function is used to establish two interesting statistical results; first, that rr
is a moment sequence for a density with decreasing failure rate, and secondly, that the likelihood ratio test for testing a simple null hypothesis in a multinomial distribution is admissible and Bayes.
An asymptotic result in traffic theory
Authors: Gani J. , Lehoczky J.
Published: July 2016

In problems of traffic theory, we are frequently concerned with the queues of vehicles which form at an intersection. A standard model is the vehicle queue whose length is increased during unit time intervals [t, t + 1) by non-negative integer inputs which form a sequence of i.i.d. or Markovian random variables; see Gani (1970) and Lehoczky ((1969), (1971)). The output from the queue at the end of each unit of time is one vehicle if the queue is non-empty, and no vehicle if there are none waiting.
Times to intermittent and to permanent failures as Brownian crossing times
Authors: Nádas Arthur
Published: July 2016

Consider a device which begins operating at time t = 0 and then operates continuously in time. The operation of the device is satisfactory so long as a physical parameter X(t) of the device remains less than a critical value c > 0 (X(0) = 0). The device does not operate satisfactorily (i.e., it is “failed”) at a time t if X(t) ≧ c. Suppose that X(t) is a random variable with mean EX(t) = ta (a> 0), i.e., the device parameter X drifts with a linear rate a.
The extinction time of a general birth and death process with catastrophes
Authors: Brockwell P. J.
Published: July 2016

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.
Extreme values of non-stationary random sequences
Authors: Hüsler Jürg
Published: July 2016

We extend some results of the extreme-value theory of stationary random sequences to non-stationary random sequences. The extremal index, defined in the stationary case, plays a similar role in the extended case. The details show that this index describes not only the behaviour of exceedances above a high level but also above a non-constant high boundary.
On limiting laws for the convex hull of a sample
Authors: Brozius Henk , De Haan Laurens
Published: July 2016

The limiting behaviour of the convex hull of a sample in is studied using the support function. Results like that of Eddy and Gale (1981) are proved without the condition of spherical symmetry from that paper.
Some properties of chord length distributions
Authors: Gates J.
Published: July 2016

The chord length distributions of planar convex sets are discussed, particularly the density values at the extremes of the range; there is a qualitative distinction between polygons and sets with smooth boundaries. The distance between convex sets is related to the distance between distribution functions.
Transience des chaines de Markov lineaires sur les permutations
Authors: Dies Jacques-Edouard
Published: July 2016

Computer scientists have introduced ‘paging algorithms' which are a special class of Markov chains on permutations known, in probability theory, as ‘libraries': books being placed on a shelf T (T is an infinite interval of the set Z of the integers) and a policy ρ : T → T such that ρ (t) < t being chosen, a book b placed at t ∊ T is selected with probability pb
, it is removed and replaced at ρ (t) prior to next removal. The different arrangements of books on the shelf are the states of the Markov chain. In this paper we prove that, if the shelf is not bounded on the left, any library (i.e. for any policy ρ and any probability ρ on the books) is transient.
The identification of ARMA processes
Authors: Hong-Zhi An , Zhao-Guo Chen
Published: July 2016

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.
Time series regression with unequally spaced data
Authors: Jones Richard H.
Published: July 2016

Regression analysis with stationary errors is extended to the case when observations are not equally spaced. The errors are modelled as either a discrete-time ARMA process with missing observations, or as a continuous-time autoregression with observational error observed at arbitrary times. Using a state-space representation, a Kalman filter is used to calculate the exact likelihood. The linear regression coefficients are separated out of the likelihood so non-linear optimization is required only with respect to the parameters modelling the error structure.
Band-limited spectral estimation of autoregressive-moving-average processes
Authors: Thomson P. J.
Published: July 2016

Consider an autoregressive-moving-average process of given order where it is known that a number of moving-average roots are of unit modulus. Such a situation might arise, for example, when a time series has been differenced to induce stationarity by removing a non-stationary polynomial or seasonal trend. A band-limited spectral estimation procedure is proposed for estimating the coefficients of such a process and the asymptotic properties of the estimators investigated. The asymptotic theory is illustrated with reference to simulated and real data. A preliminary investigation of the use of Akaike's AIC criterion and this procedure to determine the number of roots of unit modulus (in the case where this is unknown) is also carried out by means of simulation.

The proposed band-limited spectral estimation procedure can also be used to take account of other possible effects met in practice. These include, for example, the band-limited response of a recording device or trend-contaminated low-frequency components.
Testing for the presence of sinusoidal components
Authors: Quinn B. G.
Published: July 2016

Approximate and asymptotic distributional results are obtained for the likelihood ratio test of the hypothesis that a time series is composed from s sinusoidal components, at unknown frequencies, with additive Gaussian white noise, against the hypothesis that there are an additional r sinusoidal components at unknown frequencies. The work extends that of Fisher (1929), and contains a number of simulations illustrating the results.
Identification of non-linear systems using general state-dependent models
Authors: Priestley M. B. , Heravi S. M.
Published: July 2016

This paper describes an extension of the SDM scheme introduced by Priestley (1980) to the problem of the identification of non-linear systems using only input/output records. It is shown that, under quite general assumptions on the structure of the system, it is possible to identify a non-linear relationship between the input and output processes via a modified version of the Kalman-type algorithm previously applied to the study of non-linear time series models. The paper includes a numerical study of data generated from various types of non-linear systems.
Data structures—the problem of time series computing
Authors: Henstridge John
Published: July 2016

The scope of statistical packages is largely defined by the data structures supported. It is claimed that none of the standard structures used in major packages is wholly suitable for time series data and this is the major reason why time series has not benefited from modern developments in statistical computing.
An algorithm for exponential fitting revisited
Authors: Osborne M. R. , Smyth G. K.
Published: July 2016

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.
Linnik distributions and processes
Authors: Anderson Dale N. , Arnold Barry C.
Published: July 2016

Using a simple characterization of the Linnik distribution, discrete-time processes having a stationary Linnik distribution are constructed. The processes are structurally related to exponential processes introduced by Arnold (1989), Lawrance and Lewis (1981) and Gaver and Lewis (1980). Multivariate versions of the processes are also described. These Linnik models appear to be viable alternatives to stable processes as models for temporal changes in stock prices.
Some characterizations of exponential or geometric distributions in a non-stationary record value model
Authors: Witte Hans-Jürgen
Published: July 2016

Let {Fn
}
n ≧ 0 be a sequence of c.d.f. and let {Rn
}
n ≧ 1 be the sequence of record values in a non-stationary record model where after the (n − 1)th record the population is distributed according to Fn. Then the equidistribution of the nth population and the record increment Rn – Rn

– 1 (i.e. Rn – Rn

– 1
~ Fn
) characterizes Fn
to have an exponentially decreasing hazard function. To be more precise Fn
is the exponential distribution if the support of Rn

– 1 generates a dense subgroup in and otherwise the entity of all possible solutions can be obtained in the following way: let for simplicity the above additive subgroup be any c.d.f. F satisfying F(0) = 0, F(1) < 1 can be chosen arbitrarily. Setting λ = – log(1 – F(1)), Fn
(x) = 1 – F(x – [x])exp(–λ [x]) is an admissible solution coinciding with F on the interval [0, 1] ([x] denotes the integer part of x). Simple additional assumptions ensuring that Fn
is either exponential or geometric are given. Similar results for exponential or geometric tail distributions based on the independence of Rn

– 1 and Rn – Rn

– 1 are proved.
Saddlepoint approximations in conditional inference
Authors: Wang Suojin
Published: July 2016

Saddlepoint approximations are derived for the conditional cumulative distribution function and density of where is the sample mean of n i.i.d. bivariate random variables and g(x, y) is a non-linear function. The relative error of order O(n
–1) is retained. The results extend the important work of Skovgaard (1987), and are useful in conditional inference, especially in the case of small or moderate sample sizes. Generalizations to higher-dimensional random vectors are also discussed. Some examples are demonstrated.
Discretizations for the average impulse control of piecewise deterministic processes
Authors: Costa O. L. V.
Published: July 2016

This paper presents a state space and time discretization for the general average impulse control of piecewise deterministic Markov processes (PDPs). By combining several previous results we show that under some continuity, boundedness and compactness conditions on the parameters of the process, boundedness of the discretizations, and compactness of the state space, the discretized problem will converge uniformly to the original one. An application to optimal capacity expansion under uncertainty is given.
Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion
Authors: Sly Allan
Published: July 2016

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.
Genetic drift with polygamy and arbitrary offspring distribution
Authors: Cannings C.
Published: July 2016

The rate of genetic drift at an autosomal locus for a bisexual, diploid population of fixed size is studied. The generations are non-overlapping. The model encompasses a variety of mating systems, including random monogamy, random polygamy in one sex and random mating. The rate of drift is shown for several models to depend on the expected number of parents that two randomly selected individuals have in common. The male and female offspring are assigned to families in a fairly general way, which permits the study of a model in which each family has offspring of one sex only. The equation arising in this last case is identical to one of Jacquard for a system in which sib-mating is excluded.
The cost of a carrier-borne epidemic
Authors: Jerwood D.
Published: July 2016

In this paper, the cost of the carrier-borne epidemic is considered. The definition of duration, as used by Weiss (1965) and subsequent authors, is generalised and the probability distribution for the number of located carriers is obtained. One component of cost, namely the area generated by the trajectory of carriers, is examined and its probability density function derived. The expected area generated is then shown to be proportional to the expected number of carriers located during the epidemic, a result which has an analogue in the general stochastic epidemic.
Some extensions of Takács's limit theorems
Authors: Shanbhag D. N.
Published: July 2016

In this paper, we establish that if an interarrival time exceeds a service time with a positive probability then the queueing system GI/G/s with a finite waiting room always has proper limiting distributions for its characteristics such as queue length, waiting time and the remaining service times of the customers being served. The result remains valid if we consider a GI/G/s system with bounded waiting times. A technique is also given to establish that for a system with Poisson arrivals the limiting distributions of the queueing characteristics at an epoch of arrival and at an arbitrary epoch are identical.
The vectorial representation of the frequency of encounters of freely flowing vehicles
Authors: Garwood F.
Published: July 2016

It is known that if q vehicles at speed v pass a fixed point per unit time, randdomly and independently, and mix with another set q', v', then the expected number of overtakings per unit length of road per unit time is qq' (v' – v)/vv'. If k, k' are the concentrations, i.e., number per unit length of road, this rate can also be expressed as kk' (v'– v) and as q'k – qk'. It is also the expected number of intersections per unit area on the space-time diagram, where the vehicle paths are represented by sets of random parallel lines. If each set is represented by a vector with magnitude equal to the density (i.e., inverse of the spacing), the rate is equal to the magnitude of the vector product. This is extended to the general case of a stream of vehicles with distributed speeds. This has an equivalent vector, whose components are the total concentration (in the direction of the time axis) and total flow (distance direction). This leads to the concept of the cumulative vector curve in problems of geometrical probability. The extension to the case of variable flows and speeds is indicated. The vector representing the distribution of speeds is then variable, but satisfies a condition of continuity which makes its divergence vanish.
Positive columns for stochastic matrices
Authors: Isaacson Dean , Madsen Richard
Published: July 2016

If an n × n stochastic matrix has a column with no zeros, one can immediately conclude that the chain is ergodic and the state corresponding to that column is persistent and aperiodic. In this paper it is shown that it is decidable whether or not some power of a finite stochastic matrix has a positive column. Some problems regarding positive columns in infinite stochastic matrices are also considered.
Dams with random outputs
Authors: Collings P. S.
Published: July 2016

The results obtained by Lehoczky on the first emptiness of a dam subject to random outputs are extended to a more general model.
Record values and inter-record times
Authors: Shorrock R. W.
Published: July 2016

First, asymptotic results for inter-record times when the CDF of the underlying IID process is not necessarily continuous are obtained, by a stochastic order argument, from known results for the continuous case. Then the asymptotic behaviour of the bivariate process of upper-record values and inter-record times is studied. Finally, assuming continuity of the underlying CDF, we derive the law of the process of total times spent in sets of states, viewing upper record values as states and inter-record times as times spent in a state, the process so viewed being a discrete time continuous state Markov jump process.

The possible relevance of this result to single lane road traffic flow is indicated.
Necessary conditions for Markovian processes on a lattice
Authors: Moran P. A. P.
Published: July 2016

Stationary processes which are defined on the points of a square lattice and are Markovian in various senses are considered. It is shown that a certain assumption of linearity of regression forces the spectral distribution to be of a certain explicit form, and that given this form Gaussian processes of this kind are easily constructed. Certain non-Gaussian processes satisfying the various Markovian properties are also constructed and the difference from nearest-neighbour systems emphasized. It is conjectured, but not proved, that the assumption of linearity of regression also implies Gaussianity.
The heavy traffic approximation for single server queues in series
Authors: Harrison J. Michael
Published: July 2016

A tandem queue with K single server stations and unlimited interstage storage is considered. Customers arrive at the first station in a renewal process, and the service times at the various stations are mutually independent i.i.d. sequences. The central result shows that the equilibrium waiting time vector is distributed approximately as a random vector Z under traffic conditions (meaning that the system traffic intensity is near its critical value). The weak limit Z is defined as a certain functional of multi-dimensional Brownian motion. Its distribution depends on the underlying interarrival and service time distributions only through their first two moments. The outstanding unsolved problem is to determine explicitly the distribution of Z for general values of the relevant parameters. A general computational approach is demonstrated and used to solve for one special case.
On the expected range and expected adjusted range of partial sums of exchangeable random variables
Authors: Boes D. C. , Cruz J.D. Salas-La
Published: July 2016

Studies of storage capacity of reservoirs, under the assumption of infinite storage, lead to the problem of finding the distribution of the range or adjusted range of partial sums of random variables.

In this paper, formulas for the expected values of the range and adjusted range of partial sums of exchangeable random variables are presented. Such formulas are based on an elegant result given in Spitzer (1956). Some consequences of the aforementioned formulas are discussed.
Cortical salience network activation precedes the development of delusion severity
Authors: Raij T. T. , Mäntylä T. , Mantere O. , Kieseppä T. , Suvisaari J.
Published: July 2016

Background

Delusion is the most characteristic symptom of psychosis. While researchers suggested an association between changes of the cortical salience network (CSN) and delusion, whether these CSN findings are a cause or a consequence of delusion remains unknown.

Method

To assess the effect of CSN functioning to forthcoming changes in delusion scores, we measured brain activation with 3-T functional magnetic resonance imaging in two independent samples of first-episode psychosis patients (total of 27 patients and 23 healthy controls). During scanning, the patients evaluated statements about whether an individual's psychosis-related experiences should be described as a mental illness, and control statements that were also evaluated by healthy controls. Symptoms were assessed at the baseline and at 2 months follow-up with Brief Psychiatric Rating Scale.

Results

Both tasks activated the CSN in comparison with rest. Activation of CSN (‘illness evaluation v. control task’ contrast) in patients positively correlated with worsening of or less improvement in delusions at the 2-month follow-up assessment. This finding was independent of delusion and clinical insight scores at the baseline evaluation.

Conclusions

Our findings link symptom-evaluation-related CSN functioning to severity of delusion and, importantly, add a new layer of evidence for the contribution of CSN functioning to the longitudinal course of delusions.
Propulsion—The Engine Designer’s View
Authors: Pearson H.
Published: July 2016

An important point to realise in the question of propulsion for aircraft of Mach 2 and upwards is that efficiency of the power plant is no longer a problem. Due to the high pressure developed from the intake the overall pressure ratio of the engine is high, and the aircraft forward speed being high the Froude propulsive efficiency is also favourable. Fig. 1 shows, in fact, that at Mach 2 overall thermal efficiency as high as 35 per cent is achieved which, of course, compares favourably with the best electrical power station generation. Indeed, it is one of the main reasons why economic transport at high Mach numbers is possible. The falling aerodynamic efficiency, as defined by lift/ drag ratio, is offset by this rising propulsive efficiency, so that a somewhat similar overall performance is obtained as compared with subsonic aircraft.
Engineering Systems on Supersonic Aircraft
Authors: Morgan R. C.
Published: July 2016

A great deal has been said and written about the necessity to launch into a completely new standard plateau of systems engineering for supersonic, as distinct from subsonic, aircraft. So far as I have been able to gather, one reason for all this could be the argument that, as the supersonic aircraft will be so costly to operate, i.e. so uneconomical, it must be operated at a very high utilisation with very short turn-rounds and that therefore all the systems must be very much more durable than has previously been the case. Another reason could well be that the flight régimes are such that there will have to be much more dependence on certain systems, e.g. pressurisation at 70,000 ft., cabin cooling at very high speed and so on.
An Iteration Process for the Solution of the Prandtl-Meyer Expansion
Authors: Collar A. R.
Published: July 2016

In the Journal of the Royal Aeronautical Society, November 1959, the writer described an iteration process for the solution of the equations for plane oblique shock waves. Iteration methods avoid the difficulty of reading a solution from a chart; or, given a chart, provide a means of checking such a reading and, usually, of improving the accuracy to any desired degree.

As with plane oblique shocks, it is usual to use a chart to obtain the solution of a problem involving a Prandtl-Meyer expansion fan. The present note proposes an iteration process to avoid the use of a Prandtl-Meyer chart; or, given such a chart, offers the possibility of improvement in the accuracy of the solution obtained by reading from it, the limit being set by the accuracy of the trigonometric tables used.
An Observation on the use of Dimensional Analysis and Similarity Relations in Non-Uniform Heat Transfer
Authors: Barrow Henry
Published: July 2016

The theoretical study of heat transfer in ducts and passages which are not circular is difficult. In addition to geometrical and hydrodynamic problems, thermal aspects such as non-uniformity of heat transfer at the section boundary, increase the number of variables to be taken into account. The popular and perhaps simplest technique for the prediction of heat transfer in forced turbulent convection in non-circular ducts, is to use the more easily determined equation for an equivalent circular section. The form of the equation, which is used to correlate experimental data for the simpler case of heat transfer in the circular section, may be derived from considerations of similarity or alternatively by dimensional analysis. (Reference may be made to the classical work of W. Nusselt at the early part of the present century for the derivation of such an equation.) The equivalent circular pipe is equivalent in two respects. It is a pipe which has the same pressure drop and same heat transfer as the non-circular duct under consideration for the same conditions. The diameter of the equivalent pipe which replaces the non-circular section will be discussed later.
Jet Lift Engines and Power Plants for V.T.O.L. Aircraft
Authors: Wilde G. L.
Published: July 2016

The Short SCI V.T.O.L. Research Aircraft, using four special Rolls-Royce RB.108 jet lift engines, which made its first flights in 1959 heralds a new method of taking-off and landing which may revolutionise the operational flexibility of aircraft of the future. The Short SC. 1 is the result of six years research and development by Short Brothers and Harland Ltd., who built and developed the aircraft, and Rolls-Royce Ltd. who designed and developed the special light weight turbojet engines which support the aircraft during the V.T.O.L. phase and which are shut down as soon as the aircraft has attained wing borne flight by the horizontal thrust from its separate propulsion engine. The SC. 1 is shown in hovering flight in Fig. 1.