A new bivariate negative binomial distribution

A new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.     

Compound distributions with efficient computation in inventory model applications

In an inventory model, the distribution of total units demanded can be considered as a compound distribution arising from the distributions of demand occurrence and individual demand size. Three such compound distributions are considered, where the number of demands is Poisson distributed. The demand size distribution will depend on the observed or desired variance-to-mean ratio. An approximation using the gamma distribution is given in terms of the cumulants of the compound distribution for both fixed and stochastic lead times.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.     

Recurrence relations between moments of order statistics

A general result for obtaining recurrence relations between single moments of order statistics is obtained and has been used to establish the recurrence relations between moments of some doubly truncated distributions. The examples considered are Weibull, exponential, Pareto, power function, Cauchy, and logistic. Recurrence relations are also obtained for nontruncated gamma and beta distributions.     

Remarks on a univariate shock model with some bivariate generalizations

In a 1973 paper J. D. Esary, A. W. Marshall, and F. Proschan [5] considered a shock model giving rise to various nonparametric classes of life distributions of interest in reliability theory. A number of authors have extended these results in a variety of directions. In this paper, alternative proofs of the increasing failure rate (IFR) and decreasing mean residual life (DMRL) results are given which do not make use of the theory of total positivity. Some bivariate extensions are then obtained using a shock model similar to that originally used by H. W. Block, A. S. Paulson, and R. C. Kohberger [2] to unify various bivariate exponential distributions.     

Convolutions and generalization of logconcavity: Implications and applications

Additive convolution of unimodal and α‐unimodal random variables are known as an old classic problem which has attracted the attention of many authors in theory and applied fields. Another type of convolution, called multiplicative convolution, is rather younger. In this article, we first focus on this newer concept and obtain several useful results in which the most important ones is that if is logconcave then so are and for some suitable increasing functions ?. This result contains and as two more important special cases. Furthermore, one table including more applied distributions comparing logconcavity of f(x) and and two comprehensive implications charts are provided. Then, these fundamental results are applied to aging properties, existence of moments and several kinds of ordered random variables. Multiplicative strong unimodality in the discrete case is also introduced and its properties are investigated. In the second part of the article, some refinements are made for additive convolutions. A remaining open problem is completed and a conjecture concerning convolution of discrete α‐unimodal distributions is settled. Then, we shall show that an existing result regarding convolution of symmetric discrete unimodal distributions is not correct and an easy alternative proof is presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 109–123, 2016     

Single channel source separation of radar fuze mixed signal based on phase difference analysis

A new method based on phase difference analysis is proposed for the single-channel mixed signal separation of single-channel radar fuze. This method is used to estimate the mixing coefficients of de-noised signals through the cumulants of mixed signals, solve the candidate data set by the mixing coefficients and signal analytical form, and resolve the problem of vector ambiguity by analyzing the phase differences. The signal separation is realized by exchanging data of the solutions. The waveform similarity coefficients are calculated, and the time–frequency distributions of separated signals are analyzed. The results show that the proposed method is effective.     

Discrete bathtub failure rate and upside-down bathtub mean residual life

The concepts of a bathtub-shaped failure rate and upside-down bathtub-shaped mean residual life for discrete lifetime distributions are considered. The relationship between these concepts is established. The discrete counterparts of IFRA and DFRA classes discussed in the continuous case are combined into the class of a bathtub-shaped failure rate average. The relationship between bathtub-shaped failure rate and bathtub-shaped failure rate average is also given. © 1993 John Wiley & Sons, Inc.     

The estimation of P(x < Y) for distributions useful in life testing

In this paper the reliability function K = P(X < Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions. The paper is partly expository.     

基于四阶累积量的双基地MIMO雷达收发角度估计

提出了一种基于四阶累积量的双基地MIMO雷达收发角度估计算法。在接收端,通过分别构造单阵元和双阵元的四阶累积量矩阵,采用基于四阶累积量的MUSIC算法和ESPRIT算法分别估计出目标的离开方向(DOD)和波达方向(DOA),并且DOD和DOA自动配对。该算法将二维参数的估计问题转化为两个一维形式,不需要二维谱峰搜索,在保证二维方位角估计性能的基础上,降低了运算量。利用四阶累积量有效地扩展了阵列孔径,并且适用于任意加性高斯噪声环境。仿真结果验证了算法的有效性。     

Poisson分布与正态分布参数的Γ—极小极大估计

对于Poisson分布及正态分布,本文在其参数θ的先验一阶矩和二阶矩的部分信息已知的情况下,给出了θ的极小极大估计,同时也给出了最不利先验分布。     

Limiting behavior of mixtures of discrete lifetime distributions

In this article a mixture of discrete lifetime distributions is considered. Sufficient conditions are given for establishing results on the limiting behavior of the failure rate of the mixture. A connection between this limiting behavior and burn in is shown. The limiting behavior of the mean residual life of the mixture is also considered. The mixed Poisson, geometric, negative binomial, and Weibull distributions are discussed. © 1996 John Wiley & Sons, Inc.     

An approximate planning model for distributed computing networks

We develop an approximate planning model for a distributed computing network in which a control system oversees the assignment of information flows and tasks to a pool of shared computers, and describe several optimization applications using the model. We assume that the computers are multithreaded, and have differing architectures leading to varying and inconsistent processing rates. The model is based on a discrete‐time, continuous flow model developed by Graves [Oper Res 34 (1986), 522–533] which provides the steady‐state moments of production and work‐in‐queue quantities. We make several extensions to Graves' model to represent distributed computing networks. First, we approximately model control rules that are nonlinear functions of the work‐in‐queue at multiple stations through a linearization approach. Second, we introduce an additional noise term on production and show its use in modeling the discretization of jobs. Third, we model groups of heterogeneous computers as aggregate, “virtual computing cells” that process multiple tasks simultaneously, using a judiciously selected control rule. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A queuing process with bilevel hysteretic service-rate control

The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process. A bilevel hysteretic control based on queue length control levels is employed in an M/M/1 queuing system. Expressions are obtained for queue length probabilities, the first two factorial moments of queue length and two figures of merit for describing control performance under the assumption of statistical equilibrium. Computational examples illustrate the effects on queuing processes subject to this type of control. Several cost formulae are considered for comparison of costs when the queue control doctrine is varied. Situations in which hysteretic control is useful are discussed.     

Improving series and parallel systems through mixtures of duplicated dependent components

We discuss suitable conditions such that the lifetime of a series or of a parallel system formed by two components having nonindependent lifetimes may be stochastically improved by replacing the lifetimes of each of the components by an independent mixture of the individual components' lifetimes. We also characterize the classes of bivariate distributions where this phenomenon arises through a new weak dependence notion. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

基于高阶累积量与神经网络的干扰识别算法

研究了一种基于高阶累积量和神经网络的干扰识别算法。该方法把卫星通信中常见的各种干扰信号的归一化高阶累积量作为分类特征参数,应用神经网络对特征参数进行分类训练,将接收干扰信号的归一化高阶累积量输入已训练的神经网络进行干扰类型的识别。试验结果表明:该算法在低干信比的情况下具有较高的识别准确率。     

On the output of parallel exponential service channels

The paper treats the output process of a service center that has a large number of independent exponential channels in parallel. Initially all channels are working and there is a fixed backlog of items awaiting service. The moments are derived and central limit theorems are developed. Problems of computation are discussed and suitable formulae are developed. The joint distribution of the output of the center with the center's total busy time and total idle time are derived. Normal approximations to these distributions are presented.     

基于高阶累积量的滑动加窗参数型多径时延估计

针对传统方法不适合估计多径时延和难以抑制相关高斯噪声,构造了基于高级累积量的滑动加窗参数估计模型。该模型利用高阶累积量抑制高斯噪声,应用滑动窗充分利用采集数据。通过理论分析和仿真实验表明,该方法能够准确地估计时延,有效地抑制干扰和相关噪声的影响,且在性能估计方面,优于传统基于相关的方法。     

Managing waiting times of backordered demands in single‐stage (Q,r) inventory systems

We present a service constrained (Q, r) model that minimizes expected holding and ordering costs subject to an upper bound on the expected waiting time of demands that are actually backordered. We show that, after optimizing over r, the average cost is quasiconvex in Q for logconcave continuous lead time demand distributions. For logconcave discrete lead time demand distributions we find a single‐pass efficient algorithm based on a novel search stopping criterion. The algorithm also allows for bounds on the variability of the service measure. A brief numerical study indicates how the bounds on service impact the optimal average cost and the optimal (Q, r) choice. The discrete case algorithm can be readily adapted to provide a single pass algorithm for the traditional model that bounds the expected waiting time of all demands (backordered or not). © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 557–573, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10028