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This paper considers the study of the optimality of the extended design generated by adding few runs to an existing E ( χ 2 ) -optimal mixed-level supersaturated design. This paper covers the work of Gupta et al. (2010, 2012) on extended two-level and s -level supersaturated designs as two special cases. A lower bound to E ( χ 2 ) has been obtained for the proposed designs. A small example is presented here attaining the lower bound. [ABSTRACT FROM AUTHOR]

Abstract: Usually, two different types of shock models (extreme and cumulative shock models) are employed to model the dynamic risk processes. In extreme shock models, only the impact of the current fatal shock is usually taken into account, whereas, in cumulative shock models, the impact of the preceding shocks is accumulated as well. However, in practice, the effect of the corresponding shock can be realized in those two ways in one model (i.e., it can be fatal or, otherwise it is accumulated). This observation justifies the consideration of a ‘combined shock model’ in the risk modeling and analysis. In this paper, we generalize the study of the dynamic risk processes that were previously considered in the literature. The main theme of this paper is to find the optimal allocation policies for the generalized combined risk processes via the stochastic comparisons of survival functions. It will be seen that the obtained results hold for ‘general counting processes’ of shocks. In addition, we consider the problem of maximizing a gain function under certain risks and obtain reasonable decisions based on a variability measure. Furthermore, the meaningful explanations for the results on the policy ordering will be provided. [Copyright &y& Elsevier]

Abstract: In this paper we discuss testing for an interaction in the two-way ANOVA with just one observation per cell. The known results are reviewed and a simulation study is performed to evaluate type I and type II risks of the tests. It is shown that the Tukey and Mandel additivity tests have very low power in case of more general interaction scheme. A modification of Tukey''s test is developed to resolve this issue. All tests mentioned in the paper have been implemented in R package Additivity Tests. [Copyright &y& Elsevier]

Abstract: In this paper a new discrepancy measure of uniformity for uniform designs (UDs) in a unit cube is presented. Alternative measures of uniformity based on distance criteria which can be applied to higher dimensions are also discussed. The good lattice point (glp) method was used to construct the uniform designs. Two approaches (generator equivalence and projection) of reducing the computational cost of the glp method are proposed and discussed. Two examples are presented in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we are interested in the study of beta kernel density estimators from an asymptotic minimax point of view. These estimators allows to estimate density functions with support in [0,1]. It is well-known that beta kernel estimators are – on the contrary of classical kernel estimators – “free of boundary effect” and thus are very useful in practice. The goal of this paper is to prove that there is a price to pay: for very regular density functions or for certain losses, these estimators are not minimax. Nevertheless they are minimax for classical regularities such as regularity of order two or less than two, supposed commonly in the practice and for some classical losses. [Copyright &y& Elsevier]

Abstract: The usual assumptions for the average case analysis of binary search trees (BSTs) are random insertions and random deletions. If a BST is built by n random insertions the expected number of key comparisons necessary to access a node is 2ln n+O(1). This well-known result is already contained in the first papers on such ‘random’ BSTs. However, if random insertions are intermixed with random deletions the analysis of the resulting BST seems to become more intricate. At least this is the impression one gets from the related publications since 1962, and it is quite appropriate to speak of a story of errors in this context, as will be seen in the present survey paper, giving an overview on this story. [Copyright &y& Elsevier]

Abstract: In an earlier paper Srivastava [2005. Combinatorial Hermitian Algebras Derived from Latin Squares. J. Statist. Plann. Inference 129, 305–316], subsequently referred to as [S05], the author had presented an infinite class of algebras of Hermitian matrices. Each of these algebras were derived from Latin Squares. In this paper, we show how to obtain a unitary matrix (over the complex field) such that is a diagonal matrix, for all matrices belonging to a particular algebra. The notation is defined in the next paragraph. The said diagonal matrix is a matrix that contains the characteristic roots of . The matrix may be different for different algebras. Many other related results are also presented. The algebras are further discussed. How the Hermitian matrices arise in Quantum Mechanics (where every observable attribute of every physical phenomenon is in a sense characterized by a Hermitian matrix) is briefly described. The significance of the existence of Hermitian algebras and the application to Physics and Chemistry is pointed out. [Copyright &y& Elsevier]

Fang et al. (J. Statist. Plann. Inference 86 (2000b) 239) have given a method of construction of multi-level supersaturated designs. Our paper presents a new method of construction of multi-level supersaturated designs, based on Galois field theory. The supersaturated designs constructed in the paper are E(fNOD)-optimal. [Copyright &y& Elsevier]

The classic Schwarz Information Criterion, originally derived as an approximation to Bayes posterior probability, is widely used as a standalone likelihood-based measure of model fit. However, selection consistency is compromised when model sets partially include their parameter boundaries and when these in turn are partially shared by different models. This happens, for example, where sets represent mixed weak and strict inequality restrictions on parameters. To enable consistent selection of such models, a generic extension of the Schwarz criterion is required but does not appear to be available in the literature to date. In this paper, we define the boundary extended Schwarz criterion for a model to be the maximum of Schwarz-type criteria applied to the model parameter space and a systematically-generated list of boundary subsets. This entails new concepts of boundary interaction level and model dimension. A self-contained theory is presented along with examples and simulation. [ABSTRACT FROM AUTHOR]

This paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment. [ABSTRACT FROM AUTHOR]

Abstract: We give an overview of random matrix theory (RMT) with the objective of highlighting the results and concepts that have a growing impact in the formulation and inference of statistical models and methodologies. This paper focuses on a number of application areas especially within the field of high-dimensional statistics and describes how the development of the theory and practice in high-dimensional statistical inference has been influenced by the corresponding developments in the field of RMT. [Copyright &y& Elsevier]

Abstract: Blocking is an important technique to reduce the noises introduced from uncontrollable variables. Many optimal blocking schemes have been proposed in the literature but there is no single approach that can be applied to various blocked designs. In this paper, we construct a mathematical framework using the count function (or the so-called indicator function) and develop a comprehensive methodology which allows us to select various optimal blocked orthogonal arrays: regular or non-regular designs with qualitative, quantitative or mixed-type factors of two, three, higher or mixed levels. Under this framework, most existing approaches are special cases of our methodology. [Copyright &y& Elsevier]

Abstract: Foldover design is a commonly used technique that is obtained by adding another fraction to an initial fractional factorial design. Because such added designs require the same run size as the initial design, semifoldover designs that consist of half of a foldover fraction have been investigated in the recent literature for regular two-level fractional factorial designs. As the initial design and the follow-up semifoldover design are usually conducted at different stages, it is important to consider a block factor reflecting this effect. This paper studies the impact of the block factor on the semifoldover of designs. We first propose a method for obtaining the equivalent semifoldover plans. Then the properties and the structures of blocked semifoldover designs are explored. The optimal blocked semifoldover designs for 16 and 32 runs are obtained and tabulated for practical use. [Copyright &y& Elsevier]

Abstract: This paper proposes a class of optimal design criteria for prediction in linear regression models with r responses based on the volume of the rectangular confidence region, termed -optimality. A general equivalence theorem and a geometrical characterization of the R L r -optimal design are established, which are used to obtain or verify the R L r -optimality. Several examples are given for illustration. [Copyright &y& Elsevier]

Abstract: This paper derives the first two moments of the two versions of the Riesz distribution in the terms of their characteristic functions. [Copyright &y& Elsevier]

Abstract: In this paper we consider the problem of testing exponentiality against IFR alternatives. A measure of deviation from exponentiality is developed and a class of test statistics are constructed on the basis of this measure. It is shown that the test statistic is an L-statistic. The asymptotic as well as the exact distributions of the test statistics are obtained and the test statistics are proved to be consistent. The Pitman efficiency has also been studied. [Copyright &y& Elsevier]

Abstract: Zhang et al. (2008) proposed a general minimum lower order confounding (GMC for short) criterion, which aims to select optimal factorial designs in a more elaborate and explicit manner. By extending the GMC criterion to the case of blocked designs, Wei et al. (submitted for publication) proposed a B1-GMC criterion. The present paper gives a construction theory and obtains the B1-GMC designs with , where denotes a two-level regular blocked design with runs, n treatment factors, and blocks. The construction result is simple. Up to isomorphism, the B1-GMC designs can be constructed as follows: the n treatment factors and the block effects are, respectively, assigned to the last n columns and specific columns of the saturated design with Yates order. With such a simple structure, the B1-GMC designs can be conveniently used in practice. Examples are included to illustrate the theory. [Copyright &y& Elsevier]

Abstract: This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises–Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises–Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises–Fisher distributions on Stiefel manifolds. [Copyright &y& Elsevier]

Abstract: Most fractional factorial designs have no replicated points and thus do not provide a reliable estimate for experimental error. The objective of this paper is to study the issue of partially replicated two-level fractional factorial (FF) designs, thereby allowing for the unbiased estimation of the experimental error while maintaining the orthogonality of the main effects. Through the tool of indicator function and the idea of semifoldover, we propose two simple and effective techniques to produce designs with partially replicated points in general two-level FF designs, whether they are regular or not. The related properties of constructed partially replicated designs are investigated. Our results indicate that partially replicated FF are competitive in practice. [Copyright &y& Elsevier]

Abstract: This paper studies the consistency of Bayesian nonparametric regression models. We concentrate on the use of the sup metric and dealing with non-stochastic, i.e. designed, covariate values. We illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to construct covariance matrix functions whose entries are compactly supported, and to use them as building blocks to formulate other covariance matrix functions for second-order vector stochastic processes or random fields. In terms of the scale mixture of compactly supported covariance matrix functions, we derive a class of second-order vector stochastic processes on the real line whose direct and cross covariance functions are of Pólya type. Then some second-order vector random fields in whose direct and cross covariance functions are compactly supported are constructed by using a convolution approach and a mixture approach. [Copyright &y& Elsevier]

Abstract: Sometimes additive hazard rate model becomes more important to study than the celebrated (Cox, 1972) proportional hazard rate model. But the concept of the hazard function is sometimes abstract, in comparison to the concept of mean residual life function. In this paper, we have defined a new model called ‘dynamic additive mean residual life model’ where the covariates are time dependent, and study the closure of this model under different stochastic orders. [Copyright &y& Elsevier]

Abstract: This paper discusses method for constructing the prediction intervals for time series model with trend using the sieve bootstrap procedure. Gasser–Müller type of kernel estimator is used for trend estimation and prediction. The boundary modification of the kernel is applied to control the edge effect and to construct the predictor of a trend. [Copyright &y& Elsevier]

Abstract: Experiments that study complex real world systems in business, engineering and sciences can be conducted at different levels of accuracy or sophistication. Nested space-filling designs are suitable for such multi-fidelity experiments. In this paper, we propose a systematic method to construct nested space-filling designs for experiments with two levels of accuracy. The method that makes use of nested difference matrices can be easily performed, many nested space-filling designs for experiments with two levels of accuracy can thus be constructed, and the resulting designs achieve stratification in low dimensions. In addition, the proposed method can also be used to obtain sliced space-filling designs for conducting computer experiments with both qualitative and quantitative factors. [Copyright &y& Elsevier]

Abstract: Efforts have been made in the literature to find optimal single arrays which work best for the robust parameter experiments. However, examples show that in many cases the optimal designs obtained by the existing criteria cloud not attain the maximum number of clear interested effects for robust parameter experiments. In this paper, through a similar way of (ZLZA, in short), an aliasing pattern to measure the confounding between the interested effects and other effects for the case of robust parameter designs is introduced. A new criterion for selecting optimal two-level regular single arrays is proposed. In the consideration of the criterion, two rank-orders of effects are suggested: one is based on the interest of experimenters and the other is under the usual effect hierarchy principle. The optimal designs are tabulated in the appendix. [Copyright &y& Elsevier]

Abstract: This paper deals with the allocation of active redundancies to a k-out-of-n system with independent and identically distributed (i.i.d.) components in the sense of the hazard rate order. It is shown that the system''s hazard rate may be decreased by balancing the allocation of active redundancies. This generalizes the main result of and improves the corresponding one of as well. As an application, we build the reversed hazard rate order on order statistics from sample having proportional hazard rates, which strengthens the usual stochastic order in Theorem 2.1 of to the reversed hazard order in the situation that all components are of (rational) proportional hazard rates. [Copyright &y& Elsevier]

Abstract: This paper proposes a model of prior ignorance about a scalar variable based on a set of distributions . In particular, a set of minimal properties that a set of distributions should satisfy to be a model of prior ignorance without producing vacuous inferences is defined. In the case the likelihood model corresponds to a one-parameter exponential family of distributions, it is shown that the above minimal properties are equivalent to a special choice of the domains for the parameters of the conjugate exponential prior. This makes it possible to define the largest (that is, the least-committal) set of conjugate priors that satisfies the above properties. The obtained set is a model of prior ignorance with respect to the functions (queries) that are commonly used for statistical inferences; it is easy to elicit and, because of conjugacy, tractable; it encompasses frequentist and the so-called objective Bayesian inferences with improper priors. An application of the model to a problem of inference with count data is presented. [Copyright &y& Elsevier]

Abstract: The focus of this paper is objective priors for spatially correlated data with nugget effects. In addition to the Jeffreys priors and commonly used reference priors, two types of “exact” reference priors are derived based on improper marginal likelihoods. An “equivalence” theorem is developed in the sense that the expectation of any function of the score functions of the marginal likelihood function can be taken under marginal likelihoods. Interestingly, these two types of reference priors are identical. The propriety of the marginal priors and joint posteriors is studied for a large class of objective priors including all objective priors developed. Under quite general conditions, only Jeffreys-rule and “exact” reference priors yield proper posteriors. A simulation study shows that the exact reference priors perform better than the Jeffreys-rule prior. Two real spatial datasets are used for illustration. [Copyright &y& Elsevier]

Abstract: considered order preserving property of maximum likelihood estimators. In this paper there are given conditions under which the moment estimators have the property of preserving stochastic orders. The preserving property for the usual stochastic order as well as for likelihood ratio one is considered. Sufficient conditions are established for some parametric families of distributions. [Copyright &y& Elsevier]

Abstract: Mixed-level designs have become widely used in the practical experiments. When the levels of some factors are difficult to be changed or controlled, fractional factorial split-plot (FFSP) designs are often used. It is highly to know when a mixed-level FFSP design with resolution III or IV has clear effects. This paper investigates the conditions of a resolution III or IV FFSP design with both two-level and four-level factors to have various clear factorial effects, including two types of main effects and three types of two-factor interaction components. The structures of such designs are shown and illustrated with examples. [Copyright &y& Elsevier]

Abstract: The present paper deals with multi-level supersaturated designs. We present a new technique for the construction of supplementary difference sets. Based on the new supplementary difference sets, we also provide multi-level supersaturated designs with a large number of columns when compared with other designs. Moreover, these designs retain the equal occurrence property. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a system consisting of two dependent components and we are interested in the average remaining life of the component that fails last when (i) the first failure occurs at time t and (ii) the first failure occurs after time t. For both the cases, expressions are derived in the case of general bivariate normal distribution and a class of bivariate exponential distribution including bivariate exponential distribution of Arnold and Strauss, absolutely continuous bivariate exponential distribution of Block and Basu, bivariate exponential distribution of Raftery, Freund''s bivariate exponential distribution and Gumbel''s bivariate exponential distribution. [Copyright &y& Elsevier]

Abstract: It is important that the proportion of true null hypotheses be estimated accurately in a multiple hypothesis context. Current estimation methods, however, are not suitable for high-dimensional data such as microarray data. First, they do not consider the (strong) dependence between hypotheses (or genes), thereby resulting in inaccurate estimation. Second, the unknown distribution of false null hypotheses cannot be estimated properly by these methods. Third, the estimation is affected strongly by outliers. In this paper, we find out the optimal procedure for estimating the proportion of true null hypotheses under a (strong) dependence based on the Dirichlet process prior. In addition, by using the minimum Hellinger distance, the estimation should be robust to any model misspecification as well as to any outliers while maintaining efficiency. The results are confirmed by a simulation study, and the newly developed methodology is illustrated by a real microarray data. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the Berry–Esséen type bound of the sample quantiles for strong mixing sequence under some simple and weak conditions. The rates of normal approximation are shown as and under some certain conditions. [Copyright &y& Elsevier]

Abstract: In this paper, and based on a progressive type-II censored sample from the generalized Rayleigh (GR) distribution, we consider the problem of estimating the model parameters and predicting the unobserved removed data. Maximum likelihood and Bayesian approaches are used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Artificial and real data analyses have been performed for illustrative purposes. [Copyright &y& Elsevier]

Abstract: In this paper, varying coefficient models are investigated with the response and covariate prone to measurement error. Without specifying any error structure equation, four estimators of the coefficient function vector are proposed by using the local linear kernel smoothing technique and also proved to be asymptotically normal. The data-driven bandwidth selection method is discussed. Simulation examples are conducted to evaluate the proposed estimation methods. [Copyright &y& Elsevier]

Abstract: The paper uses the empirical likelihood method to study the construction of confidence intervals and regions for regression coefficients and response mean in generalized linear models with missing response. By using the inverse selection probability weighted imputation technique, the proposed empirical likelihood ratios are asymptotically chi-squared. Our approach is to directly calibrate the empirical likelihood ratio, which is called as a bias-correction method. Also, a class of estimators for the parameters of interest is constructed, and the asymptotic distributions of the proposed estimators are obtained. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths/areas of confidence intervals/regions. An example of a real data set is used for illustrating our methods. [Copyright &y& Elsevier]

Abstract: Let be an arbitrary lattice path, called in this context string, consisting of two kinds of steps (rises and falls) and let j be a non-negative integer. In this paper, the explicit formula for the generating function F j associated with the Dyck path statistic “number of occurrences of at height j” is evaluated. For the expression of F j some basic characteristics of the string are used, namely its number of rises, height, depth and periodicity, as well as the generating function of the Catalan numbers. [Copyright &y& Elsevier]

Abstract: Inspired by the ideas of column and row juxtaposition in and level transformation in , this paper presents a new method for constructing optimal supersaturated designs (SSDs). This method provides a convenient way to construct mixed-level designs with relatively large numbers of levels, avoiding the blind search and numerous calculations by computers. The goodness of the resulting SSDs is judged by the ( and ) and J 2 () criteria. Some nice properties of the new designs are also provided. [Copyright &y& Elsevier]

Abstract: proportional hazard (PH) model has been used to model failure time data in Reliability and Survival Analysis. Recently, proportional reversed hazard model has been analyzed in the literature. Sometimes, the hazard rate (or the reversed hazard rate) may not be proportional over the whole time interval, but may be proportional differently in different intervals. In order to take care of this kind of problems, in this paper, we introduce the dynamic proportional hazard rate model, and the dynamic proportional reversed hazard rate model, and study their properties for different aging classes. The closure of the models under different stochastic orders has also been studied. Examples are presented to illustrate different properties of the models. [Copyright &y& Elsevier]

Abstract: The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. Although the corresponding linear combination of the unbiased estimators is minimax under the restricted problem, it has a drawback of taking values outside the restricted parameter space. Thus, it is reasonable to use the linear combination of the restricted estimators such as maximum likelihood or truncated estimators. In this paper, a necessary and sufficient condition for such restricted estimators to be minimax is derived, and it is shown that the restricted estimators are not minimax when the number of the location parameters is large. The condition for minimaxity is examined for some specific distributions. Finally, similar problems of estimating the product and sum of the restricted scale parameters are studied, and it is shown that analogous non-dominance properties appear when the number of the scale parameters is large. [Copyright &y& Elsevier]

Abstract: In this paper, we propose to include Weibull tail-distributions in a more general family of distributions. In particular, the considered model also encompasses the whole Fréchet maximum domain of attraction as well as log-Weibull tail-distributions. The asymptotic normality of some tail estimators based on the log-spacings between the largest order statistics is established in a unified way within the considered family. This result permits to understand the similarity between most estimators of the Weibull tail-coefficient and the Hill estimator. Some different asymptotic properties, in terms of bias, rate of convergence, are also highlighted. [ABSTRACT FROM AUTHOR]

Abstract: In a latin square of order n, a k-plex is a selection of kn entries in which each row, column and symbol occurs k times. A 1-plex is also called a transversal. An indivisible k-plex is one that contains no c-plex for . For orders , existence of latin squares with a partition into 1-plexes was famously shown in 1960 by Bose, Shrikhande and Parker. A main result of this paper is that, if k divides n and then there exists a latin square of order n with a partition into indivisible k-plexes. Define to be the largest integer k such that some latin square of order n contains an indivisible k-plex. We report on extensive computations of indivisible plexes and partitions in latin squares of order at most 9. We determine exactly for and find that . Up to order 8 we count all indivisible partitions in each species. For each group table of order we report the number of indivisible plexes and indivisible partitions. For group tables of order 9 we give the number of indivisible plexes and identify which types of indivisible partitions occur. We will also report on computations which show that the latin squares of order 9 satisfy a conjecture that every latin square of order n has a set of disjoint 2-plexes. By extending an argument used by Mann, we show that for all there is some for which there exists a latin square of order n that has k disjoint transversals and a disjoint (n−k)-plex that contains no c-plex for any odd c. [ABSTRACT FROM AUTHOR]

Abstract: Neighbor balance designs were first introduced by in circular blocks for the use in serological research. Subsequently several researchers have defined the neighbor designs in different ways. In this paper, neighbor balance circular designs for (k≤v) block size are constructed for even number of treatments i.e. v=2n. No such series of designs is known in literature. Two theorems are developed for circular designs. gives the non-binary circular blocks, whereas generates binary circular blocks when n≤4 and non-binary blocks for n>4. In suggested designs no treatment is ever a neighbor of itself. Blocks are constructed in such a way that each treatment is a right and left neighbor of every other treatment for a fixed number of times say λ. Sizes of initial circular blocks are not same. One main guiding principle for such designs is to ensure economy in material use. [Copyright &y& Elsevier]

Abstract: have recently introduced power-sequence terraces. In this paper we have used these terraces for the construction of some new families of balanced cross-over designs of first and second order which are variance-balanced. We have also used them for the construction of some new families of balanced ternary cross-over designs. [Copyright &y& Elsevier]

Abstract: When preparing data for public release, information organizations face the challenge of preserving the quality of data while protecting the confidentiality of both data subjects and sensitive data attributes. Without knowing what type of analyses will be conducted by data users, it is often hard to alter data without sacrificing data utility. In this paper, we propose a new approach to mitigate this difficulty, which entails using Bayesian additive regression trees (BART), in connection with existing methods for statistical disclosure limitation, to help preserve data utility while meeting confidentiality requirements. We illustrate the performance of our method through both simulation and a data example. The method works well when the targeted relationship underlying the original data is not weak, and the performance appears to be robust to the intensity of alteration. [Copyright &y& Elsevier]

Abstract: The construction of optimal 2 n−m designs with , where N=2 n−m is the run size, and their comparison under different criteria have received significant attention in recent years. In this paper, we first prove that the MaxC2 design with n=N/4+1 is unique up to isomorphism and has general minimum lower order confounding (GMC). Then, by utilizing the theory of doubling and second order saturated resolution IV designs extended by , we propose a method of constructing GMC design and obtain all the GMC designs with up to isomorphism. Finally, we show that, for all N and n in the above range, the MA and GMC designs are different. [Copyright &y& Elsevier]

Abstract: The paper revisits the concept of a power series distribution by defining its series function, its power parameter, and hence its probability generating function. Realization that the series function for a particular distribution is a special case of a recognized mathematical function enables distributions to be classified into families. Examples are the generalized hypergeometric family and the q-series family, both of which contain generalizations of the geometric distribution. The Lerch function (a third generalization of the geometric series) is the series function for the Lerch family. A list of distributions belonging to the Lerch family is provided. The advantage of classifying power series distributions into families is that distributions within a family can be expected to have analogous properties which depend on the mathematical properties of the series function. This is demonstrated by focussing on equilibrium birth and death processes for the Lerch family. [Copyright &y& Elsevier]

Abstract: In this paper we study the class of skew Dyck paths, i.e. of those lattice paths that are in the first quadrant, begin at the origin, end on the x-axis, consist of up steps , down steps , and left steps , and such that up steps never overlap with left steps. In particular, we show that these paths are equinumerous with several other combinatorial objects, we describe some involutions on this class, and finally we consider several statistics on . [Copyright &y& Elsevier]

Abstract: In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto–Hahn model or systems with preemptive priorities. [Copyright &y& Elsevier]