Parameter estimations for generalized exponential distribution under progressive type-I interval censoring

The estimates, via maximum likelihood, moment method and probability plot, of the parameters in the generalized exponential distribution under progressive type-I interval censoring are studied. A simulation is conducted to compare these estimates in terms of mean squared errors and biases. Finally, these estimate methods are applied to a real data set based on patients with plasma cell myeloma in order to demonstrate the applicabilities.     

A generalized method of moments for closed queueing networks

We introduce a new solution technique for closed product-form queueing networks that generalizes the Method of Moments (MoM), a recently proposed exact algorithm that is several orders of magnitude faster and memory efficient than the established Mean Value Analysis (MVA) algorithm. Compared to MVA, MoM recursively computes higher-order moments of queue lengths instead of mean values, an approach that remarkably reduces the computational costs of exact solutions, especially on models with large numbers of jobs.In this paper, we show that the MoM recursion can be generalized to include multiple recursive branches that evaluate models with different numbers of queues, a solution approach inspired by the Convolution algorithm. Combining the approaches of MoM and Convolution simplifies the evaluation of normalizing constants and leads to large computational savings with respect to the recursive structure originally proposed for MoM.     

The distribution of sums, products and ratios for Lawrance and Lewis's bivariate exponential random variables

We derive the exact distributions of R=X+Y, P=XY and W=X/(X+Y) and the corresponding moment properties when X and Y follow Lawrence and Lewis's bivariate exponential distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables—obtained using intensive computing power—will be of use to practitioners of the bivariate exponential distribution.     

Software reliability prediction model based on support vector regression with improved estimation of distribution algorithms

Software reliability prediction plays a very important role in the analysis of software quality and balance of software cost. The data during software lifecycle is used to analyze and predict software reliability. However, predicting the variability of software reliability with time is very difficult. Recently, support vector regression (SVR) has been widely applied to solve nonlinear predicting problems in many fields and has obtained good performance in many situations; however it is still difficult to optimize SVR's parameters. Previously, some optimization algorithms have been used to find better parameters of SVR, but these existing algorithms usually are not fully satisfactory. In this paper, we first improve estimation of distribution algorithms (EDA) in order to maintain the diversity of the population, and then a hybrid improved estimation of distribution algorithms (IEDA) and SVR model, called IEDA-SVR model, is proposed. IEDA is used to optimize parameters of SVR, and IEDA-SVR model is used to predict software reliability. We compare IEDA-SVR model with other software reliability models using real software failure datasets. The experimental results show that the IEDA-SVR model has better prediction performance than the other models.     

A bootstrap goodness of fit test for the generalized Pareto distribution

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter γ. The proposed test is an intersection–union test which tests separately the cases of γ≥0 and γ<0 and rejects if both cases are rejected. If the test does not reject, then it is known whether the shape parameter γ is either positive or negative. A Monte Carlo simulation experiment was conducted to assess the power of performance of the intersection–union test. The GPd hypothesis was tested on a data set containing Mexico City’s ozone levels. ¹     

Approximating the distribution of goodness of fit tests for discrete data

The Berry-Esseen theorem is used to study the error of the normal approximation to the distribution of several goodness of fit tests for discrete data. A practical bound is proposed and confirmed by simulations.     

Size distribution and waiting times for the avalanches of the Cell Network Model of Fracture

The Cell Network Model is a fracture model recently introduced that resembles the microscopical structure and drying process of the parenchymatous tissue of the Bamboo Guadua angustifolia. The model exhibits a power-law distribution of avalanche sizes, with exponent −3.0 when the breaking thresholds are randomly distributed with uniform probability density. Hereby we show that the same exponent also holds when the breaking thresholds obey a broad set of Weibull distributions, and that the humidity decrements between successive avalanches (the equivalent to waiting times for this model) follow in all cases an exponential distribution. Moreover, the fraction of remaining junctures shows an exponential decay in time. In addition, introducing partial breakings and cumulative damages induces a crossover behavior between two power-laws in the histogram of avalanche sizes. This results support the idea that the Cell Network Model may be in the same universality class as the Random Fuse Model.     

Maximum-likelihood estimation for the multivariate Sarmanov distribution: simulation study

Used to model dependency in a multivariate setting with given marginals, Sarmanov's family of distributions creates difficulties when it comes to statistical inference. In this paper, we study maximum-likelihood procedures for estimating Sarmanov's distribution parameters for two different models: Under model I, we make use of a random data sample of volume m observed from an n-dimensional random vector, while model II consists of the first n dependent univariate random variables from a discrete-time stochastic process to which we try to fit Sarmanov's distribution starting from the corresponding n-tuple of observed values. To estimate some specific parameters, the use of the method of moments based on the covariance/correlation coefficient is also suggested. We illustrate these methods on simulated data and discuss the results.     

An improved cuckoo search algorithm for the problem of electric distribution network reconfiguration

Power loss reduction has an important role in operating electric distribution network system. There are a lot of methods for reduction power loss such as capacitor placement, distributed generation placement and electric distribution network reconfiguration (EDNR). Among these methods, the EDNR is an efficient technique to reduce power loss due to without taking any costs. However, the EDNR problem is a nonlinear, discrete problem and lots of extreme points. Therefore, it is necessary to have efficient methods for solving the EDNR problem. In this paper, an improved cuckoo search algorithm (ICSA) is proposed for solving the EDNR problem. In which, based on disadvantages of exploration and exploitation process of cuckoo search algorithm (CSA) for solving the EDNR problem, a local search mechanism is added to exploit candidate solutions existing around the current best solution. The calculated results on the simple distribution networks to complex distribution networks show that ICSA has ability for finding the global optimal solution with much smaller iterations and better quality of obtained solution compared with CSA and some other improved versions of CSA. The performance comparisons with other existing methods available in previous studies and the software of Power System Simulator/Advanced Distribution Engineering Productivity Tool (PSS/ADEPT) also lead to the better electric distribution network configuration with smaller total power losses. As a result, ICSA is a potential and reliable method for solving the EDNR problems.     

Estimating the width of a uniform distribution when data are measured with additive normal errors with known variance

The problem of estimating the width of the symmetric uniform distribution on the line when data are measured with normal additive error is considered. The main purpose is to discuss the efficiency of the maximum likelihood estimator and the moment method estimator. It is shown that the model is regular and that the maximum likelihood estimator is more efficient than the moment method estimator. A sufficient condition is also given for the existence of both estimators.     

Estimating and quantifying the impact of using models for integration and testing

Industrial trends show that the lead time and costs of integrating and testing high-tech multi-disciplinary systems are becoming critical factors for commercial success. In our research, we developed a method for early, model-based integration and testing to reduce this criticality.Although its benefits have been demonstrated in industrial practice, the method requires certain investments to achieve these benefits, e.g. time needed for creating models. Making the necessary trade-off between investments and potential benefits to decide when modeling is profitable is a difficult task that is often based on personal intuition and experience. In this paper, we describe a method based on integration and test sequencing techniques that can be used to make quantitative impact estimations of using models for integration and testing.An industrial case study application of this method shows that it is feasible to quantify the costs and benefits of using models in terms of risk, time, and costs, such that the profitability can be determined.     

Use of multiple models and qualitative knowledge for on-line moving horizon disturbance estimation and fault diagnosis

An integrated fault detection, fault isolation, and parameter estimation technique is presented in this paper. Process model parameters are treated as disturbances that dynamically affect the process outputs. A moving horizon estimation technique minimizes the error between process and model measurements over a finite horizon by calculating model parameter values across the estimation horizon. To implement qualitative process knowledge, this minimization is constrained such that only a limited number of different faults (parameters) may change during a specific horizon window. Multiple linear models are used to capture nonlinear process characteristics such as asymmetric response, variable dynamics, and changing gains. Problems of solution multiplicity and computational time are addressed. Results from a nonlinear chemical reactor simulation are presented.     

Physically accurate nonlinear models for fault detection and diagnosis: the case of a power plant

This paper deals with two main contributions. The first is the definition of an accurate nonlinear model of a section of a real 320 MW power plant. Within the framework of this global method, the second contribution is the modelling of the most common faults that may occur in plants like the one considered in the paper. All these models allow the simulation of the system both under normal working conditions and under anomalous conditions due to the occurrence of one of the faults modelled. The simulated model can be integrated with the automation system of the plant and used in real time, thus providing the plant technicians with crucial information on the plant behaviour, for instance, fault detection and diagnosis can be accomplished in a natural way. Simulation results and comparisons with real data show the effectiveness of the proposed approach.     

An iterative Kalman smoother/least-squares algorithm for the identification of delta-ARX models

Additive measurement noise on the output signal is a significant problem in the δ-domain and disrupts parameter estimation of auto-regressive exogenous (ARX) models. This article deals with the identification of δ-domain linear time-invariant models of ARX structure (i.e. driven by known input signals and additive process noise) by using an iterative identification scheme, where the output is also corrupted by additive measurement noise. The identification proceeds by mapping the ARX model into a canonical state-space framework, where the states are the measurement noise-free values of the underlying variables. A consequence of this mapping is that the original parameter estimation task becomes one of both a state and parameter estimation problem. The algorithm steps between state estimation using a Kalman smoother and parameter estimation using least squares. This approach is advantageous as it avoids directly differencing the noise-corrupted ‘raw’ signals for use in the estimation phase and uses different techniques to the common parametric low-pass filters in the literature. Results of the algorithm applied to a simulation test problem as well as a real-world problem are given, and show that the algorithm converges quite rapidly and with accurate results.     

Box-Jenkins模型偏差补偿方法与其他辨识方法的比较

对于存在相关噪声干扰的Box—Jenkins系统,本文借助于偏差补偿原理,推导了一个偏差补偿最小二乘(BCLS)辨识方法;理论分析说明BCLS方法能够给出系统模型参数的无偏估计,并将提出的方法与递推增广最小二乘算法和递推广义增广最小二乘算法进行了比较研究;用仿真试验分析了这些算法的各自特点和适用范围。     

“Anti-Bayesian” parametric pattern classification using order statistics criteria for some members of the exponential family

This paper submits a comprehensive report of the use of order statistics (OS) for parametric pattern recognition (PR) for various distributions within the exponential family. Although the field of parametric PR has been thoroughly studied for over five decades, the use of the OS of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented earlier for the uniform distribution and for some members of the exponential family, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. Apart from the results for the Gaussian and doubly exponential which are merely cited here, our new results include the Rayleigh, Gamma and certain Beta distributions. The new scheme, referred to as classification by moments of order statistics (CMOS), has an accuracy that attains Bayes' bound for symmetric distributions, and is, otherwise, very close to the optimal Bayes' bound, as has been shown both theoretically and by rigorous experimental testing. The results here also give a theoretical foundation for the families of border identification (BI) algorithms reported in the literature.     

An improved multiobjective estimation of distribution algorithm for environmental economic dispatch of hydrothermal power systems

Environmental economic dispatch of fixed head of hydrothermal power systems is viewed as a mulitobjective optimization problem in this paper. The practical hydrothermal system possesses various constraints which make the problem of finding global optimum difficult. This paper develops an improved multiobjective estimation of distribution algorithm to solving the above problem. A local learning operation is added into the original regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) in the improved approach so as to improve the local search ability and enhance the convergence efficiency. Furthermore, a repair mechanism is employed to repair the searched infeasible solutions in order to be able to search in the feasible region. In the experiment, the results obtained by the proposed approach have been compared with those from other three MOEAs: NSGA-II, NNIA, and RM-MEDA. Results from some pervious reported methods have also been employed to compare with our method. In addition, the results demonstrate the superiority of this proposed method as a promising MOEA to solve this power system multiobjective optimization problem.     

An adaptive and computationally efficient algorithm for parameters estimation of superimposed exponential signals with observations missing randomly

In this paper, we consider the parameters estimation of a model of superimposed exponential signals in multiplicative and additive noise when some observations are missing randomly. The least squares estimators (LSEs) and asymptotic Cramer–Rao low bound (ACRLB) for the considered model are studied and the asymptotic distributions of the LSEs for parameters of frequencies, phases and amplitudes of the considered model are also derived and obtained. An adaptive and computationally efficient iterative algorithm is proposed to estimate the frequencies of the considered model. It can be seen that the iterative algorithm works quite well in terms of biases and mean squared errors and the refined estimators by three iterations are observed to be asymptotically unbiased and consistent. The statistics for iteration are designed to change adaptively according to different missing distributions of time points so as to keep the estimators of frequencies to be asymptotically unbiased. Moreover, the proposed estimators attain the same convergence rate and asymptotic distribution as those of LSEs which are used to obtain the confident intervals and coverage probabilities of the frequencies for finite sample. Since the iterative algorithm needs only three iterations to work, it saves much computation time. So the proposed estimators are LSEs equivalent while avoid the heavy computation cost of LSEs. Finally, several simulation experiments are performed to verify the effectiveness of the proposed algorithm. To examine the robustness of the proposed algorithm, we also test the algorithm on the dual tone multi-frequency (DTMF) signal with observations missing in block and symmetric α-stable (SaS) noise condition, as well as on sinusoidal frequency modulated signals.     

A statistical model of fracture for a 2D hexagonal mesh: The Cell Network Model of Fracture for the bamboo Guadua angustifolia

A 2D, hexagonal in geometry, statistical model of fracture is proposed. The model is based on the drying fracture process of the bamboo Guadua angustifolia. A network of flexible cells are joined by brittle junctures of fixed Young moduli that break at a certain thresholds in tensile force. The system is solved by means of the Finite Element Method (FEM). The distribution of avalanche breakings exhibits a power law with exponent −2.93(9), in agreement with the random fuse model (Bhattacharyya and Chakrabarti, 2006) [1].