对数收益率的偏斜Logistic分布与VaR估计

本文通过直方图和Q-Q图的直观方法展示了上证指数和深证指数的对数收益率具有尖峰厚尾和偏斜的分布特征,利用Shapiro-Wilk正态性检验和Kolmogorov-Smirnov检验等方法检验了对数收益率的分布与正态分布有显著性差异,并以较大的概率水平接受了对数收益率服从偏斜Logistic分布,同时给出了基于偏斜Logistic分布的VaR风险量的估计,结果显示上证指数的风险小于深证指数的风险。     

An optimal time to sleep for an auto-sleep system considering multi-usage states

An auto-sleep system is defined by the following two properties:

• 1.(i) a call for the system occurs randomly and intermittently
• 2.(ii) the system automatically goes to sleep if there occurs no call during a prespecified time T.

It considers four states:

• 1.(a) sleep
• 2.(b) warm-up
• 3.(c) nonusage
• 4.(d) usage.

For such a system, the time to sleep has been discussed based on suitable criteria. This study extends the model for an auto-sleep system so that the model can deal with multi-usage states. With a view to determining an optimal time to sleep under the extended model, the expected energy consumed per unit time is formulated as a criterion to be minimized. The existence of an optimal time to sleep is examined under a general call distribution. Numerical examples are also provided for a Weibull as well as a log-normal call distribution.     

Detecting tail behavior: mean excess plots with confidence bounds

In many practical situations exploratory plots are helpful in understanding tail behavior of sample data. The Mean Excess plot is one of the exploratory tools often used in practice to understand the right tail behavior of a data set. It is known that if the underlying distribution of a data sample is in the maximum domain of attraction of a Fréchet, a Gumbel or a Weibull distributions then the ME plot of the data approaches a straight line in an appropriate sense, with positive, zero or negative slope respectively. In this paper we construct confidence intervals around the ME plots which assist us in ascertaining which particular maximum domain of attraction the data set comes from. We recall weak limit results for the Fréchet domain of attraction, already obtained in Das and Ghosh (Bernoulli 19, 308–342 2013) and derive weak limits for the Gumbel and Weibull domains in order to construct confidence bounds. We demonstrate our methodology by applying them to simulated and real data sets.     

Generation of Over-Dispersed and Under-Dispersed Binomial Variates

Abstract

This article proposes an algorithm for generating over-dispersed and under-dispersed binomial variates with specified mean and variance. The over-dispersed/under-dispersed distributions are derived from correlated binary variables with an underlying continuous multivariate distribution. Different multivariate distributions or different correlation matrices result in different over-dispersed (or under-dispersed) distributions. The over-dispersed binomial distributions that are generated from three different correlation matrices of a multivariate normal are compared with the beta-binomial distribution for various mean and over-dispersion parameters by quantile-quantile (Q-Q) plots. The two distributions appear to be similar. The under-dispersed binomial distribution is simulated to model an example data set that exhibits under-dispersed binomial variation.     

A generalized log-normal distribution and its goodness of fit to censored data

In life testing experiments, the skewed distributions like log-normal, Weibull, gamma and generalized gamma are the most suitable models for recording the failure time measurements. In this paper, a generalized version of log-normal distribution is proposed and its goodness-of-fit for a randomly censored data set representing the remission times of bladder cancer patients has been demonstrated and compared with other lifetime models considered in the literature. The P-P plots of Kaplan-Meier estimator against the survival functions of the considered models are used to show the goodness-of-fit. A simulation study is also performed to estimate the parameters in both the classical and Bayesian setups.     

多元威布尔分布形状参数相等的似然比检验

将多元威布尔分布形状参数相等的检验转化为多元极值分布尺度参数相等的检验,利用Logistic模型的似然比统计量,给出相关参数为0．3,0．5,0．8时,检验统计量的模拟分位数和功效,指出相关参数越小,似然比统计量的功效越大。     

A generalization of Norton's theorem for queueing networks

A general framework for aggregation and decomposition of product form queueing networks with state dependent routing and servicing is presented. By analogy with electrical circuit theory, the stations are grouped into clusters of subnetworks such that the process decomposes into a global process and a local process. Moreover, the local process factorizes into the subnetworks. The global process and the local processes can be analyzed separately as if they were independent. The global process describes the behaviour of the queuing network in which each cluster is aggregated into a single station, whereas the local process describes the behaviour of the subnetworks as if they are not part of the queueing network. The decomposition and aggregation method formalized in this paper allows us to first analyze the global behaviour of the queueing network and subsequently analyze the local behaviour of the subnetworks of interest or to aggregate clusters into single stations without affecting the behaviour of the rest of the queueing network. Conditions are provided such that:

- the global equilibrium distribution for aggregated clusters has a product form;

- this form can be obtained by merely monitoring the global behaviour;

- the computation of a detailed distribution, including its normalizing constant, can be decomposed into the computation of a global and a local distribution;

- the marginal distribution for the number of jobs at the stations of a cluster can be obtained by merely solving local behaviour.

As a special application, Norton's theorem for queueing networks is extended to queueing networks with state dependent routing such as due to capacity constraints at stations or at clusters of stations and state dependent servicing such as due to service delays for clusters of stations.     

Method of primers in calculating the probability of destruction of a unidirectional composite material in tension

A method of primers is elaborated which allows one to calculate the distribution function of durability of a composite material in tension in the reinforcement direction. Integral and differential equations for calculating the probabilities of formation of primers and destruction of a material caused by their formation are presented. Distribution functions of material strength for the parameter of Weibull distribution of fiber strength on the interval 2.1 ≤ β _f ≤ 50.1 are calculated. From the functions, the average values and root-mean-square deviations of material strength are found. The results obtained agree well with calculations by using the structural-imitation simulation. The distribution functions of material strength with a high precision are approximated by the three-parameter Weibull distributions. The distribution parameters are approximated by the linear functions of ln (β_f). __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 823–838, November–December, 2007.     

Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations

We study the first-order bifurcating autoregressive process X_t=?X_⌊t/2⌋+?_t with Weibull innovations. Using point process technique, we estimate the model parameter ? and the tail index α in the Weibull distribution and obtain the joint limit distribution of estimators.     

Multivariate distributions having Weibull properties

Random variables X₁ ,…, X_n are said to have a joint distribution with Weibull minimums after arbitrary scaling if min_i(a_iX_i) has a one dimensional Weibull distribution for arbitrary constants a_i > 0, i = 1,…, n. Some properties of this class are demonstrated, and some examples are given which show the existence of a number of distributions belonging to the class. One of the properties is found to be useful for computing component reliability importance. The class is seen to contain an absolutely continuous Weibull distribution which can be generated from independent uniform and gamma distributions.     

Determining the optimal place and capacity of spare parts warehouses in the construction industry

In the construction industry, places, capacities and levels of demand in basic spare parts are changing in relatively short periods of time. This creates an optimization problem of the following form.We are given the following:o

1. (i)The location and the level of demand for each basic spare part in each work site for a specific time period.
2. (ii)The places and the levels of demand can be altered.
3. (iii)There are more than one supplier of each part geografically distributed.
4. (iv)The number of basic equipment spare parts.
5. (v)The transportation cost per load of spare parts.
6. (vi)The purchasing and functioning cost of the various air houses used as warehouses of spare parts.

In this paper we present an algorithm which determines the place, capacity and number of supply points to minimize the total cost of the supply system under the constraints (i) to (vi) above.     

A note on the sampling distribution of the information content of the priority vector of a consistent pairwise comparison judgment matrix of AHP

The sampling distribution of the information content (entropy) of the priority vector of a consistent pairwise comparison judgment matrix, PCJM(n) using the Analytic Hierarchy Process (AHP) is studied by Noble and Sanchez, where n is the number of criteria associated with the matrix. They concluded simulation experiments with sample size of 1000 and found that the distribution is normal for n=4,5,...,15. When we increased the sample size to 2000, to 3000,..., to 8000, we found that the sampling distribution of entropy is not normal for all n, n=4,5,...,15. By using BestFit software system and using sample sizes of 8000, we found that the best-fitted and the second-best-fitted distributions of the entropy are either Weibull or normal for n?4. If we consider the most number of best fitted distributions as the criteria, then Weibull should be considered as the sampling distribution of the entropy for n?4. For n=3, beta should be considered as the best-fitted distribution.     

Improved OR education through the use of spreadsheet models

The first and major part of this presentation shows how OR education may be improved through the use of spreadsheets, with several examples:

• •in decision theory, where the drawing capabilities of Excel are used to represent decision trees and where window switching and macros allow the educator to animate his presentation;
• •in linear programming, where the solver is used (remarks are made relating to the adequacy of the solver's solutions), and where the spreadsheet's graphing capabilities are used both to represent the feasible set and the objective function, and to interactively animate the objective function or constraint movements;
• •in dynamic programming, deterministic or stochastic, where it is shown that several standard spreadsheet functions facilitate the development of specialized models;
• •in simulation, where it will be seen how stochastic simulation may be facilitated through the use of an add-in, and how a decision support system may thus be built from scratch in less than 10 minutes.

A creative use of the spreadsheet in business OR models is presented in the second part of this presentation, with an example in process simulation: airport luggage traffic simulation. A short third part presents the possibilities offered by spreadsheet add-ins.     

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are

1. classical circuit switch telephone networks (loss networks) and
2. present-day wireless mobile networks.

Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it does not have one in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hypercubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to

• upper bounds for loss probabilities and
• analytic error bounds for the accuracy of the approximation for various performance measures.

The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:

• pure loss networks as under (i)
• GSM networks with fixed channel allocation as under (ii).

The results are of practical interest for computational simplifications and, particularly, to guarantee that blocking probabilities do not exceed a given threshold such as for network dimensioning.     

An Application of Stochastic Programming with Weibull Distribution–Cluster Based Optimum Allocation of Recruitment in Manpower Planning

Abstract

Recruitment of persons for various assignments with required talents in an organization is an important feature, since it plays a vital role in the growth of the organization. To achieve the required expertise in recruitment, in this paper Linear Stochastic Programming (LSP) is applied along with cluster analysis technique. The aim of this paper is to obtain an optimal allocation of persons to different jobs, so that the time taken to complete all the jobs is minimum. The time taken for a person to complete a job is assumed to follow Weibull distribution. The parameters of Weibull distribution is obtained through Maximum Likelihood Estimator (MLE) approach, along with Cohen's iterative process.     

Quasi-linear production systems: Optimisation of the transportation system

This paper is devoted to the quasi-linear production systems under the following additional hypothesis:

• 1.1. There exists a loading sequence which gives the input order of the parts of the system.
• 2.2. There exists, for each machine, a processing sequence which gives the order for manufacturing the parts.
• 3.3. The transportation system uses carts. A cart is a transportation unit able to carry one part for a machine to another. The parts are loaded on the carts before entering the system and unloaded when the manufacture of the part is finished.

We give an algorithm which leads to the minimal number of carts needed in order to reach the maximal production rate, the loading and processing sequences being known. We also characterize the optimal solution in the case of equal processing times.     

Modelling the motion of a three-link manipulator based on a plane with a time-dependent inclination

This work deals with the modelling of a three-link manipulator mounted on a plane with a time-dependent inclination. Two cases are considered.

• (i)The plane is part of a rigid body.
• (ii)The plane is in a moored ship.

     

Exact and approximation methods for dependability assessment of tram systems with time window

The transportation system examined in this paper is the city tram one, where failed trams are replaced by reliable spare ones. If failed tram is repaired and delivered, then it comes back on work. There is the time window that failed tram has to be either replaced (exchanged) by spare or by repaired and delivered within. Time window is therefore paramount to user perception of transport system unreliability. Time between two subsequent failures, exchange time, and repair together with delivery time, respectively, are described by random variables A, E, and D. A/E/D is selected as the notation for these random variables. There is a finite number of spare trams. Delivery time does not depend on the number of repair facilities. Hence, repair and delivery process can be treated as one with infinite number of facilities. Undesirable event called hazard is the event: neither the replacement nor the delivery has been completed in the time window. The goal of the paper is to find the following relationships: hazard probability of the tram system and mean hazard time as functions of number of spare trams. For systems with exponential time between failures, Weibull exchange and exponential delivery (so M/W/M in the proposed notation) two accurate solutions have been found. For systems with Weibull time between failures with shape in the range from 0.9 to 1.1, Weibull exchange and exponential delivery (i.e. W/W/M) a method yielding small errors has been provided. For the most general and difficult case in which all the random variables conform to Weibull distribution (W/W/W) a method returning moderate errors has been given.     

Numerische Simulation durch Wirbel zu bestimmender Strömungsfelder im Schaufelgitter

Wir benutzen die Weierstraßschen elliptischen Funktionen und die hyperbolischen Funktionen, um die von Wirbeln hervorgerufenen Strömungsfelder zu berechnen. Die Berechnungsgebiete sind:

1. a parallelogramm bounded by four boundaries
2. a channel restricted by upper and lower boundaries
3. a half region confined by upper, lower and left boundaries.

The method of vortex distribution in a calculation plane and the calculated results are also shown. The loci of the vortices and velocity vectors show a reasonable behavior. It is concluded that this method is effective in analysing the secondary flows with vortices in a cascade.     

Advanced comminution modelling: Part 2 - Mills

This second part paper explores rock breakage mechanisms, the life cycle of rocks in mills and the strong influence of end walls on charge motion within mills. We present recent advances in particle-based modelling of mills for comminution focused around wear and the effect of slurry and slurry phase grinding. Three mill scenarios are considered:

• 1.Media flow and the resulting wear evolution of the belly and end wall liners and the resulting change in mill performance for a full industrial scale dry ball mill (modelled using DEM)
• 2.Axial slurry transport and mixing in a wet overflow industrial scale ball mill (modelled using fully coupled DEM and SPH)
• 3.Effect of mill speed on slurry and solid charge motion and the resulting grinding of fine particles in a 1.8 m diameter wet Hardinge pilot mill (modelled using fully coupled DEM and SPH with advection-diffusion-population balance equations solved for the slurry size distribution for each SPH particle)

These demonstrate the nature and level of fidelity that is now possible to include in particle-scale comminution models. They provide insights into the critical importance of curtain flows generated by the end walls of tumbling mills, on wear behaviour on liners, on the structure of slurry pools and mill discharge and on the adverse effect on grinding of increasing mill speed.