E-Bayesian estimation for the Lomax distribution based on type-II censored data

This paper is concerned with using the E-Bayesian method for computing estimates of the unknown parameter and some survival time parameters e.g. reliability and hazard functions of Lomax distribution based on type-II censored data. These estimates are derived based on a conjugate prior for the parameter under the balanced squared error loss function. A comparison between the new method and the corresponding Bayes and maximum likelihood techniques is conducted using the Monte Carlo simulation.     

Burr Type XII 分布的统计推断

该文讨论了两参数 Burr Type XII 分布基于逐次定数截尾样本的参数估计, 导出了有关参数的点估计和区间估计. 我们利用模拟方法对所给点估计和参数的最大似然估计作了比较, 模拟结果显示所给点估计优于常用的最大似然估计. 最后, 用一个实际例子说明本文所给方法.     

复合LINEX对称损失下BurrⅫ分布参数的Bayes估计

在复合LINEX对称损失函数下,研究BurrⅫ分布参数的Bayes估计和E-Bayes估计,并通过随机数值模拟检验参数的Bayes估计和E-Bayes估计的合理性及优良性.     

Bayesian estimation for generalized exponential distribution based on progressive type-I interval censoring

In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive type-I interval censoring. The Bayesian estimates of parameters and reliability function cannot be obtained as explicit forms by applying squared error loss and Linex loss functions, respectively; thus, we present the Lindley’s approximation to discuss these estimations. Then, the Bayesian estimates are compared with the maximum likelihood estimates by using the Monte Carlo simulations.     

A closed form type reduction method for piecewise linear interval type-2 fuzzy sets

In this study, a new centroid type reduction method is proposed for piecewise linear interval type-2 fuzzy sets based on geometrical approach. The main idea behind the proposed method relies on the assumption that the part of footprint of uncertainty (FOU) of an interval type-2 fuzzy set (IT2FS) has a constant width where the centroid is searched. This constant width assumption provides a way to calculate the centroid of an IT2FS in closed form by using derivative based optimization without any need of iterations. When the related part of FOU is originally constant width, the proposed method finds the accurate centroid of an IT2FS; otherwise, an enhancement can be performed in the algorithm in order to minimize the error between the accurate and the calculated centroids. Moreover, only analytical formulas are used in the proposed method utilizing geometry. This eliminates the need of using discretization of an IT2FS for the type reduction process which in return naturally improves the accuracy and the computation time. The proposed method is compared with Enhanced Karnik–Mendel Iterative Procedure (EKMIP) in terms of the accuracy and the computation time on seven test fuzzy sets. The results show that the proposed method provides more accurate results with shorter computation time than EKMIP.     

Assessing the lifetime performance index of Rayleigh products based on the Bayesian estimation under progressive type II right censored samples

Lifetime performance assessment is important in service (or manufacturing) industries. Hence, lifetime performance index C_L is used to measure the potential and performance of a process, where L is the lower specification limit. In this paper, assuming the conjugate prior distribution and squared-error loss function, this study constructs a Bayes estimator under the Rayleigh distribution with the progressive type II right censored sample. The Bayes estimator of C_L is then utilized to develop a credible interval in the condition of known L. Moreover, we also propose a Bayesian test to assess the lifetime performance of products. Finally, we give two examples and the Monte Carlo simulation to assess the behavior of the lifetime performance index C_L. Moreover, the purchasers can then employ the credible interval and the Bayesian test to determine whether the product performance adheres to the required level.     

Improved confidence intervals for the scale parameter of Burr XII model based on record values

In this paper some different sorts of confidence intervals are considered for the scale parameter of the Burr type XII distribution based on the upper record values. In this regard, the coverage probability is adopted as a measure of improvement when the endpoints are the same for all types of confidence intervals. Proposed confidence intervals are based on the preliminary test estimator, Thompson shrinkage estimator and Bayes estimator with conjugate prior information. It is nicely demonstrated that the confidence intervals based on the above methodologies are superior to the equal tail confidence interval on specific intervals. Subsequently, to construct a uniformly dominant confidence interval, the result of Kubokawa (Ann Stat 22(1):290–299, 1994) is extended for dependent observations by making use of the information that exists in a covariate record value.     

Monte carlo estimation of the sampling distribution of nonlinear model parameter estimators

The sampling distribution of parameter estimators can be summarized by moments, fractiles or quantiles. For nonlinear models, these quantities are often approximated by power series, approximated by transformed systems, or estimated by Monte Carlo sampling. A control variate approach based on a linear approximation of the nonlinear model is introduced here to reduce the Monte Carlo sampling necessary to achieve a given accuracy. The particular linear approximation chosen has several advantages: its moments and other properties are known, it is easy to implement, and there is a correspondence to asymptotic results that permits assessment of control variate effectiveness prior to sampling via measures of nonlinearity. Empirical results for several nonlinear problems are presented.This research was supported in part by the Office of Naval Research under Contract N00014-79-C-0832.     

Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution

The Weibull distribution is one of the most important distributions that is utilized as a probability model for loss amounts in connection with actuarial and financial risk management problems. This paper considers the Weibull distribution and its quantiles in the context of estimation of a risk measure called Value-at-Risk (VaR). VaR is simply the maximum loss in a specified period with a pre-assigned probability level. We attempt to present certain estimation methods for VaR as a quantile of a distribution and compare these methods with respect to their deficiency (Def) values. Along this line, the results of some Monte Carlo simulations, that we have conducted for detailed investigations on the efficiency of the estimators as compared to MLE, are provided.     

Bayesian source detection and parameter estimation of a plume model based on sensor network measurements

We consider a network of sensors that measure the intensities of a complex plume composed of multiple absorption–diffusion source components. We address the problem of estimating the plume parameters, including the spatial and temporal source origins and the parameters of the diffusion model for each source, based on a sequence of sensor measurements. The approach not only leads to multiple‐source detection, but also the characterization and prediction of the combined plume in space and time. The parameter estimation is formulated as a Bayesian inference problem, and the solution is obtained using a Markov chain Monte Carlo algorithm. The approach is applied to a simulation study, which shows that an accurate parameter estimation is achievable. Copyright © 2010 John Wiley & Sons, Ltd.     

A new model for classifying inputs and outputs and evaluating the performance of DMUs based on translog output distance function

In conventional data envelopment analysis it is assumed that the input versus output status of each chosen performance measures is known. In some conditions finding a statue of some variables from the point view of input or output is very difficult; these variables treat as both an input and output and are called flexible measures. This paper proposes a new model based on translog output distance function for classifying inputs and outputs and evaluating the performance of decision-making units by considering flexible measures. Monte Carlo simulation is applied to evaluate the presented model comparing with that of the recent model found in the literature. The result shows that the measure efficiencies of our model are statistically closer to true efficiencies and have higher rank correlation with true efficiencies. Also results obtained from simulated data show that there are high correlation between our model and that of the recent model.     

Poisson分布下基于鞍点逼近的慢性病风险差的置信区间构造

风险差是流行病学中重要的指标之一,常用来比较两种治疗或两种诊断的有效性.因此,风险差区间的精确估计对流行病病情的诊断以及治疗方案的选择有很重要的意义.结合Poisson抽样的优点以及慢性病发病周期长和发病率低的特点,利用鞍点逼近方法来构造了Poisson分布下风险差的置信区间.同时,通过实例和Monte Carlo模拟对传统的四种区间构造方法进行评价.模拟结果表明:在小样本情况下,鞍点逼近方法得到的置信区间大多数能保证覆盖率近似于期望的置信水平并且使得区间长度最短,是一种很好的置信区间构造方法.     

基于纵向数据的Poisson-Gamma模型系数的随机性检验

应用随机系数化方法对纵向数据的Poisson-Gamma回归模型进行了研究,采用Laplace展开方法得到了关于响应变量的近似似然函数并得到模型系数的随机性检验的Score统计量.通过Monte Carlo模拟分析了检验的渐近功效.最后把得到的检验统计量应用到具体的数值实例分析中说明其有效性.     

A differential harmony search based hybrid interval type2 fuzzy EGARCH model for stock market volatility prediction

In this paper a new hybrid model integrating an interval type2 fuzzy logic system (IT2FLS) with a computationally efficient functional link artificial neural network (CEFLANN) and an Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model has been proposed for accurate forecasting and modeling of financial data with changing variance over time. The proposed model denoted as IT2F-CE-EGARCH helps to enhance the ability of EGARCH model through a joint estimation of the important features of EGARCH like leverage effect, asymmetric shock by leverage effect with the secondary membership functions of interval type2 TSK FLS and the functional expansion and learning component of a CEFLANN. The secondary membership functions with upper and lower limits of IT2FLS provide a forecasting interval for handling more complicated uncertainties involved in volatility forecasting compared to type1 FLS. The performance of the proposed model has been observed with two membership functions i.e. Gaussian with fixed mean, uncertain variance and Gaussian with fixed variance and uncertain mean. The proposed model has also been compared with a few other fuzzy time series models and GARCH family models based on four performance metrics: MSFE, RMSFE, MAFE and Rel MAE. Again a differential harmony search (DHS) algorithm has been suggested for optimizing the parameters of all the fuzzy time series models. The results indicate that the proposed IT2F-CE-EGARCH model offers significant improvements in volatility forecasting performance in comparison with all other specified models over BSE Sensex and CNX Nifty dataset.     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

Behaviour of queueing approximations based on sample moments

We investigate moment–based queueing approximations in the presence of sampling error. Let L be the steady–state mean number in the system for a GI/M/1 queue. We focus on the estimation of L under the assumption that only sample moments of the interarrival–time distribution are known. A simulation experiment is carried out for several interarrival–time distributions. For each case, sample moments from the interarrival–time distribution are matched to an approximating phase–type distribution and the corresponding estimate L is obtained. We show that the sampling error in the moments induces bias as well as variability in L. Based on our simulation experiment, we suggest matching only two moments when the sample coefficient of variation is low or when sample size is low; otherwise, matching three moments is preferable.     

A multi-period stochastic portfolio optimization model applied for an airline company in the EU ETS

This paper aims to set up and solve a multi-period stochastic portfolio optimization model from an airline company’s point of view, considering all the specific European Union Emissions Trading Scheme (EU ETS) regulatory, managerial and trading constraints (i.e. physical constraints). Our contribution to existing academic literature is multiple. As the first ever case, we apply this technique to the aviation sector, a newly included sector within the EU ETS. More than mainly incorporating physical and technical (‘engineering’) features and focusing on short-term planning issues, we particularly address financial features and focus on mid-term planning issues. Therefore, instead of using spot prices, we run Monte Carlo simulations of correlated geometric Brownian motions (GBM) for traded futures prices of various emission allowance types for different CO₂ delivery time periods. We thereby specifically refer to the existing exchange-traded emission allowance types EU Emission Allowance (EUA) and Certified Emission Reduction (CER). By implementing actually valid and real-world-oriented regulatory constraints for EU ETS, namely managerial and trading constraints, our model implies a real-life application. We also highlight the possibility of banking and borrowing of emission allowances between CO₂ compliance periods, which is a crucial regulatory feature of EU ETS.     

Numerical solutions comparison for interval linear programming problems based on coverage and validity rates

In this paper, two-step method (TSM), alternative solution method (SOM-2) and best-worst case (BWC) method are introduced to solve a type of interval linear programming (ILP) problem. To compare the performance of the methods, Monte Carlo simulation is also used to solve the same ILP problem, whose solutions are assumed to be real solutions. In the comparison, two scenarios corresponding with two assumptions of distribution functions are considered: (i) all the input parameters obey normal distribution; (ii) all the input parameters obey uniform distribution. Based on the simulation results, coverage rate (CR) and validity rate (VR) are proposed as new indicators to measure the quality of the numerical solutions obtained from the methods. Results from a numerical case study indicate that the TSM and SOM-2 solutions can cover the majority of valid values (CR > 50%, VR > 50%), compared to the conventional BWC method. In addition, from the point of CR, TSM is more applicable since the solutions of TSM can identify more feasible solutions. However, from the point of VR, SOM-2 is preferred since it can exclude more baseless solutions (this means more feasible solutions are contained in the SOM-2 solutions). In general, TSM would be preferred when only the range of the system objective needs to be determined, while SOM-2 would be much useful in identifying the effective values of the objective.     

A methodology for stochastic inventory models based on a zero‐adjusted Birnbaum‐Saunders distribution

The Birnbaum–Saunders (BS) distribution is receiving considerable attention. We propose a methodology for inventory logistics that allows demand data with zeros to be modeled by means of a new discrete–continuous mixture distribution, which is constructed by using a probability mass at zero and a continuous component related to the BS distribution. We obtain some properties of the new mixture distribution and conduct a simulation study to evaluate the performance of the estimators of its parameters. The methodology for stochastic inventory models considers also financial indicators. We illustrate the proposed methodology with two real‐world demand data sets. It shows its potential, highlighting the convenience of using it by improving the contribution margins of a Chilean food industry. Copyright © 2015 John Wiley & Sons, Ltd.