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In classical Marshall–Olkin type shock models and their modifications a system of two or more components is subjected to shocks that arrive from different sources at random times and destroy the components of the system. With a distinctive approach to the Marshall–Olkin type shock model, we assume that if the magnitude of the shock exceeds some predefined threshold, then the component, which is subjected to this shock, is destroyed; otherwise it survives. More precisely, we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution. This approach allows to meet requirements of many real life applications of shock models, where the magnitude of shocks is an important factor that should be taken into account. A new class of bivariate distributions, obtained in this work, involve the joint distributions of shock times and their magnitudes. Dependence properties of new bivariate distributions have been studied. For different examples of underlying bivariate distributions of lifetimes and shock magnitudes, the joint distributions of lifetimes of the components are investigated. The multivariate extension of the proposed model is also discussed.

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... Marshall-Olkin type distributions have been of great interest in recent years. Ozkut and Bayramoglu [2] introduced a Marshall-Olkin type distribution with effect of shock magnitude. Okasha and Kayid [3] introduced a new family of Marshall-Olkin extended generalized linear exponential distribution. ...

... According to the new model, a system that consists of two components is subject to shocks that may arrive from three different sources. A shock that is produced by source 1 (2) only affects component 1 (2) while the shock that is produced by source 3 may affect both components. The produced shocks are classified as critical or non-critical. ...

In this paper, a new shock model called Marshall–Olkin run shock model is defined and studied. According to the model, two components are subject to shocks that may arrive from three different sources, and component i fails when it is subject to k consecutive critical shocks from source i or k consecutive critical shocks from source 3, i=1,2. Reliability and mean residual life functions of such components are studied when the times between shocks follow phase-type distribution.

... The MOBW distribution also has a correlation control parameter, which may be used to express the relationship of dependent competing risks. Ozkut and Bayramoglu [41] discussed the problem of the MO type distributions with effect of shock magnitude. Feizjavadian and Hashemi [18] analyzed the problem of dependent competing risks in the presence of the progressive hybrid censoring by using the MOBW distribution, and gave two illustrative examples based on the practical data sets. ...

Over the past two decades, a significant part of the statistical literature has been devoted to offer distinct univariate distributions belonging to the Marshall-Olkin family of distributions. It is because this family enjoys attractive statistical properties, providing consistently better fit than other generalized distributions with the same parental models, as well as wider applications. In this article, we provide a brief review of recent developments in Marshall-Olkin type distributions.

... Several distributions were constructed by the same way, for example, Muhammed (2016) introduced the bivariate inverse Weibull distribution. Different extensions for the Marshall-Olkin family were presented, see for example, Sarhan and Balakrishnan (2007), Jose et al. (2011), Li and Pellerey (2011), Ozkut and Bayramoglu (2014), and Davarzani et al. (2015). Barreto-Souza and Lemonte (2013) introduced the bivariate Kumaraswamy (BK) distribution, which can be applied in several reliability models like shock model, maintenance model and stress model. ...

Analyzing time to event data arises in a number of fields such as Biology and Engineering. A 8 common feature of this data is that, the exact failure time for all units may not be observable. 9 Accordingly, several types of censoring were presented. Progressive censoring allows units to 10 be randomly removed before the terminal point of the experiment. Marshall-Olkin bivariate 11 lifetime distribution was first introduced in 1967 using the exponential distribution. Recently, 12 bivariate Marshall-Olkin Kumaraswamy lifetime distribution was derived. This paper derives the 13 likelihood function under progressive type-I censoring for the bivariate Marshall-Olkin family in 14 general and applies it on the bivariate Kumaraswamy lifetime distribution. Maximum likelihood 15 estimators of model parameters were derived. Simulation study and a real data set are presented 16 to illustrate the proposed procedure. Absolute bias, mean square error, asymptotic confidence 17 intervals, confidence width and coverage probability are obtained. Simulation results indicate 18 that the mean square error is smaller and confidence width is narrower and more precise when 19 number of removals gets smaller. Also, increasing the terminal point of the experiment results 20 in reducing the mean square error and confidence width. 21

... In recent years, Marshall-Olkin shock models have been of great interest. A Marshall-Olkin type distribution including effect of shock magnitude was introduced by [2]. [3] considered Marshall-Olkin type shock model in Coherent systems. ...

... In modelling natural catastrophic events, it is logical to assume a dependence between the intensity of the catastrophe and the time elapsed since the previous catastrophe [14]. Ozkut and Bayramoglu (Bairamov) [15] studied Marshall-Olkin type shock model with the assumption that if the magnitude of the shock exceeds some prede ned threshold, then the component, which is subjected to this shock, is destroyed; otherwise it survives. More precisely, they assumed that the shock time and the magnitude of the shock are dependent random variables with a bivariate distribution. ...

In this paper, a generalized class of run shock models associated with a bivariate sequence {(X i , Y i )} i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X 1 , X 2 , ... over time, let the random variables Y 1 , Y 2 , ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑ Nt=1 Y t , where N is a stopping time for the sequence {X i } i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {X i , 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.

... Furthermore, the MOBW distribution has a correlation control parameter, which may be used to express the relationship of dependent competing risks. Ozkut and Bayramoglu (2014) discussed the problem of Marshall-Olkin type distribution with effect of shock magnitude. Feizjavadian and Hashemi (2015) analyzed the problem of dependent competing risks in the presence of progressive hybrid censoring using Marshall-Olkin bivariate Weibull distribution, and given two illustrative examples based on real dataset. ...

There are several failure modes may cause system failed in reliability and survival analysis. It is usually assumed that the causes of failure modes are independent each other, though this assumption does not always hold. Dependent competing risks modes from Marshall-Olkin bivariate Weibull distribution under Type-I progressive interval censoring scheme are considered in this paper. We derive the maximum likelihood function, the maximum likelihood estimates, the 95% Bootstrap confidence intervals and the 95% coverage percentages of the parameters when shape parameter is known, and EM algorithm is applied when shape parameter is unknown. The Monte-Carlo simulation is given to illustrate the theoretical analysis and the effects of parameters estimates under different sample sizes. Finally, a data set has been analyzed for illustrative purposes.

... The stress-strength reliability of a consecutive k-out-of-n system has been studied in [9]. Recent works on multi-component stress strength reliability are in [10][11][12][13]. ...

This paper investigates the stress–strength reliability in the presence of fuzziness. The fuzzy membership function is defined as a function of the difference between stress and strength values, and the fuzzy reliability of single unit and multicomponent systems are calculated. The inclusion of fuzziness in the stress–strength interference enables the user to make more sensitive analysis. Illustrations are presented for various stress and strength distributions.

This paper is a short review of classical and recent results on Marshall–Olkin shock models and their applications in reliability analysis. The classical Marshall–Olkin shock model was introduced in Marshall and Olkin (J Am Stat Assoc 62:30–44, 1967). The model describes a joint distribution of lifetimes of two components of a system subjected to three types of shocks. The distribution has absolutely continuous and singular parts. The Marshall–Olkin copula also aroused the interest of researchers working on the theory of copulas as an example of a copula having absolutely continuous and singular parts. There are some recent papers considering general models and modifications constructed on the basic idea of Marshall and Olkin (1967). These works find wide applications in reliability analysis in the case of a general system having n (\(n > 2\)) components and shocks coming from m (\(m > 3\)) sources. Some applications can also be seen in the theory of credit risk, where instead of lifetimes of the components, one considers the times to the default of two counter-parties subject to three independent underlying economic or financial events. In this work, we analyze and describe the results dealing with the generalization and modification of the Marshall–Olkin model.

In this article, we study an integral transformation of the copula function. We prove that under certain conditions, the studied integral transformation is also the copula function. Some properties of the integral transformation of a copula function are studied. Also we derive bounds for Kendall’s tau and Spearman’s rho.

Reliability assessment of system suffering from random shocks is attracting a great deal of attention in recent years. Excluding internal factors such as aging and wear-out, external shocks which lead to sudden changes in the system operation environment are also important causes of system failure. Therefore, efficiently modeling the reliability of such system is an important applied problem. A variety of shock models are developed to model the inter-arrival time between shocks and magnitude of shocks. In a cumulative shock model, the system fails when the cumulative magnitude of damage caused by shocks exceed a threshold. Nevertheless, in the existing literatures, only the magnitude is taken into consideration, while the source of shocks is usually neglected. Using the same distribution to model the magnitude of shocks from different sources is too critical in real practice. To this end, considering a system subject to random shocks from various sources with different probabilities, we develop a generalized cumulative shock model in this article. We use phase-type distribution to model the variables, which is highly versatile to be used for modeling quantitative features of random phenomenon. We will discuss the reliability characteristics of such system in some detail and give some clear expressions under the one-dimensional case. Numerical example for illustration is also provided along with a summary.

This paper considers the constant-partially accelerated life tests for series system products, where dependent M-O bivariate exponential distribution is assumed for the components.
Based on progressive type-II censored and masked data, the maximum likelihood estimates for the parameters and acceleration factors are obtained by using the decomposition approach. In addition, this method can also be applied to the Bayes estimates, which are too complex to obtain as usual way. Finally, a Monte Carlo simulation study is carried out to verify the accuracy of the methods under different masking probabilities and censoring schemes.

We consider coherent systems subjected to Marshall-Olkin type shocks coming at random times and destroying components of the system. The paper combines two important models, coherent systems and Marshall-Olkin type shocks and studies the mean residual life (MRL) and the mean inactivity time (MIT) functions of coherent systems that is subjected to random shocks. The considered models and theoretical results are supported with examples and graphical representations. (C) 2016 Published by Elsevier B.V.

A way to transform a given copula by means of a univariate function is presented. The resulting copula can be interpreted as the result of a global shock affecting all the components of a system modeled by the original copula. The properties of this copula transformation from the perspective of semi–group action are presented, together with some investigations on the impact on the tail behavior. Finally, the whole methodology is applied to model risk assessment.

In this paper we introduce a new probability model known as type 2 Marshall–Olkin bivariate Weibull distribution as an extension
of type 1 Marshall–Olkin bivariate Weibull distribution of Marshall–Olkin (J Am Stat Assoc 62:30–44, 1967). Various properties
of the new distribution are considered. Bivariate minification processes with the two types of Weibull distributions as marginals
are constructed and their properties are considered. It is shown that the processes are strictly stationary. The unknown parameters
of the type 1 process are estimated and their properties are discussed. Some numerical results of the estimates are also given.
KeywordsType 1 and type 2 Marshall–Olkin bivariate Weibull distribution–Marshall–Olkin bivariate exponential distribution–Bivariate minification process–Stationary process–Estimation

A model incorporating the effect of a common environment on several components (structurally independent) of a system is developed. A multivariate generalization of the Lomax (Pareto type 2) distribution is obtained by mixing exponential variables. Its relationship to other multivariate distributions is discussed. Several properties of this distribution are reported and their usefulness in reliability theory indicated. Finally, a further generalization of this multivariate Lomax distribution is presented.

This paper investigates properties of a new parametric distribution generated by Marshall and Olkin (199712.
Marshall , A. W. ,
Olkin , I. ( 1997 ). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families . Biometrika 84 : 641 – 652 . [CrossRef], [Web of Science ®]View all references) extended family of distributions based on the Lomax model. We show that the proposed distribution can be expressed as a compound distribution with mixing exponential model. Simple sufficient conditions for the shape behavior of the density and hazard rate functions are given. The limiting distributions of the sample extremes are shown to be of the exponential and Fréchet type. Finally, utilizing maximum likelihood estimation, the proposed distribution is fitted to randomly censored data.

The two-parameter generalized exponential distribution has been used recently quite extensively to analyze lifetime data. In this paper the two-parameter generalized exponential distribution has been embedded in a larger class of distributions obtained by introducing another shape parameter. Because of the additional shape parameter, more flexibility has been introduced in the family. It is observed that the new family is positively skewed, and has increasing, decreasing, unimodal and bathtub shaped hazard functions. It can be observed as a proportional reversed hazard family of distributions. This new family of distributions is analytically quite tractable and it can be used quite effectively to analyze censored data also. Analyses of two data sets are performed and the results are quite satisfactory.

Univariate Pareto distributions are extensively studied. In this article, we propose a Bayesian inference methodology in the context of multivariate Pareto distributions of the second kind (Mardia's type). Computational techniques organized around Gibbs sampling with data augmentation are proposed to implement Bayesian inference in practice. The new methods are shown to work well in artificial examples involving a trivariate distribution, and to an empirical application involving daily exchange rate data for four major currencies.

An extension of FGM class of bivariate distributions with given marginals is presented. For Huang-Kotz FGM distributions
some theorems characterizing symmetry and conditions for independence are obtained. The new family of distributions allows
us to achieve correlation between the components greater than 0.5.

Die Familie der austauschbaren Marshall-Olkin Verteilungen wird untersucht. Aus analytischer Sicht werden Querverbindungen mit vollständig monotonen Zahlenfolgen aufgezeigt. Aus wahrscheinlichkeitstheoretischer Sicht wird eine alternative Konstruktion erweiterbarer Marshall-Olkin Verteilungen mittels Lévy Subordinatoren hergeleitet. Dieses Resultat wird verwendet um effiziente Simulationsalgorithmen und ein Bewertungsmodell für Portfolio-Kreditderivate zu entwickeln.

DOI: 10.1029/2007WR006737 In this paper, the accuracy performance of monthly streamflow forecasts is discussed when using data-driven modeling techniques on the streamflow series. A crisp distributed support vectors regression (CDSVR) model was proposed for monthly streamflow prediction in comparison with four other models: autoregressive moving average (ARMA), K-nearest neighbors (KNN), artificial neural networks (ANNs), and crisp distributed artificial neural networks (CDANN). With respect to distributed models of CDSVR and CDANN, the fuzzy C-means (FCM) clustering technique first split the flow data into three subsets (low, medium, and high levels) according to the magnitudes of the data, and then three single SVRs (or ANNs) were fitted to three subsets. This paper gives a detailed analysis on reconstruction of dynamics that was used to identify the configuration of all models except for ARMA. To improve the model performance, the data-preprocessing techniques of singular spectrum analysis (SSA) and/or moving average (MA) were coupled with all five models. Some discussions were presented (1) on the number of neighbors in KNN; (2) on the configuration of ANN; and (3) on the investigation of effects of MA and SSA. Two streamflow series from different locations in China (Xiangjiaba and Danjiangkou) were applied for the analysis of forecasting. Forecasts were conducted at four different horizons (1-, 3-, 6-, and 12-month-ahead forecasts). The results showed that models fed by preprocessed data performed better than models fed by original data, and CDSVR outperformed other models except for at a 6-month-ahead horizon for Danjiangkou. For the perspective of streamflow series, the SSA exhibited better effects on Danjingkou data because its raw discharge series was more complex than the discharge of Xiangjiaba. The MA considerably improved the performance of ANN, CDANN, and CDSVR by adjusting the correlation relationship between input components and output of models. It was also found that the performance of CDSVR deteriorated with the increase of the forecast horizon. Author name used in this publication: K. W. Chau

Marshall-Olkin bivariate semi-Pareto distribution (MO-BSP) and Marshall-Olkin bivariate Pareto distribution (MO-BP) are introduced and studied. AR(1) and AR(k) time series models are developed with minification structure having MO-BSP stationary marginal distribution. Various characterizations are investigated. Copyright Springer-Verlag 2004

Recently it has been observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms. Several properties of this distribution have been discussed. We suggest to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters and also obtain the observed and expected Fisher information matrices. One data set has been re-analyzed and it is observed that the bivariate generalized exponential distribution provides a better fit than the bivariate exponential distribution.

A new class of bivariate distributions is presented in this paper. The procedure used in this paper is based on a latent random variable with exponential distribution. The model introduced here is of Marshall-Olkin type. A mixture of the proposed bivariate distributions is also discussed. The results obtained here generalize those of the bivariate exponential distribution present in the literature.

A model incorporating the effect of a common environment on several components (structurally independent) of a system is developed. A multivariate generalization of the Lomax (Pareto type 2) distribution is obtained by mixing exponential variables. Its relationship to other multivariate distributions is discussed. Several properties of this distribution are reported and their usefulness in reliability theory indicated. Finally, a further generalization of this multivariate Lomax distribution is presented.

SUMMARY A new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used two-parameter families of life distributions as the Weibull, gamma and lognormal distributions. In addition, the general method is applied to yield a new three-parameter Weibull distribution. Families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family. Bivariate versions are also considered.

This article extends A. W. Marshall and I. Olkin’s bivariate exponential distribution [ibid. 62, 30-44 (1967; Zbl 0147.381)] such that it is absolutely continuous and need not be memoryless. The new marginal distribution has an increasing failure rate, and the joint distribution exhibits an aging pattern. It offers an advantage in separately identifying the shock arrival rates and their impacts. Regarding estimation of the model, both maximum likelihood and method-of- moments-type estimation are considered. The former is more efficient but computationally more demanding, whereas the latter is simpler in computation but less efficient. The trade-off between computational burden and efficiency is gauged through Monte Carlo simulations, and it turns out to be favorable for the method-of-moments-type estimation.

The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution. © Australian Statistical Publishing Association Inc. 1999. Published by Blackwell Publishers Ltd.

This article extends Marshall and Olkin's bivariate exponential distribution such that it is absolutely continuous and need not be memoryless. The new marginal distribution has an increasing failure rate, and the joint distribution exhibits an aging pattern. It offers an advantage in separately identifying the shock arrival rates and their impacts. Regarding estimation of the model, both maximum likelihood and method-of-moments-type estimation are considered. The former is more efficient but computationally more demanding, whereas the latter is simpler in computation but less efficient. The trade-off between computational burden and efficiency is gauged through Monte Carlo simulations, and it turns out to be favorable for the method-of-moments-type estimation.

A bivariate distribution is not determined by the knowledge of the margins. Two bivariate distributions with exponential margins are analyzed and another is briefly mentioned.In the first distribution (2.1) the conditional expectation of one variable decreases to zero with increasing values of the other one. The coefficient of correlation is never positive and lies in the interval –.40≤ρ≤0, and the correlation ratio varies from –.48 to zero.In the second distribution (3.4) the conditional expectation of one variable increases or decreases with increasing values of the other variable depending on the sign of the correlation. The coefficient of correlation lies in the interval –.25≤ρ≤.25, and the correlation ratio is proportional to the coefficient.

Artificial Neural Networks (ANNs) have been successfully employed for predicting and forecasting groundwater levels up to some time steps ahead. In this paper, we present an application of feed forward neural networks (FFNs) for long period simulations of hourly groundwater levels in a coastal unconfined aquifer sited in the Lagoon of Venice, Italy. After initialising the model with groundwater elevations observed at a given time, the developed FNN should able to reproduce water level variations using only the external input variables, which have been identified as rainfall and evapotranspiration. To achieve this purpose, the models are first calibrated on a training dataset to perform 1-h ahead predictions of future groundwater levels using past observed groundwater levels and external inputs. Simulations are then produced on another data set by iteratively feeding back the predicted groundwater levels, along with real external data. The results show that the developed FNN can accurately reproduce groundwater depths of the shallow aquifer for several months. The study suggests that such network can be used as a viable alternative to physical-based models to simulate the responses of the aquifer under plausible future scenarios or to reconstruct long periods of missing observations provided past data for the influencing variables is available.
Keywords: Artificial neural networks; Groundwater levels; Coastal aquifer system; Venice lagoon; Simulation

In this paper, we discuss the problem of estimating reliability (R) of a component based on maximum likelihood estimators
(MLEs). The reliability of a component is given byR=P[Y. Here X is a random strength of a component subjected to a random stress(Y) and (X,Y) follow a bivariate pareto(BVP) distribution. We obtain an asymptotic normal(AN) distribution of MLE of the reliability(R).

Bivariate Pareto distributions arise naturally when it comes to comparing the performances of two systems. In this note, explicit expressions are derived for a relative measure of performance for every known bivariate Pareto distribution. The calculations involve the use of Gauss hypergeometric function.

We consider a bivariate Pareto distribution, as a generalization of the Lindley-Singpurwalla model, by incorporating the influence of the operating conditions on a two-component dependent system. The properties of the model and its applications to reliability analysis are discussed. © 1993 John Wiley & Sons, Inc.

A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serves to indicate conditions under which the distribution is appropriate. Two of these derivations are based on “shock models,” and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution.For this distribution, the moment generating function is obtained, comparison is made with the case of independence, the distribution of the minimum is discussed, and various other properties are investigated. A multivariate Weibull distribution is obtained through a change of variables.

Recently Sarhan and Balakrishnan [2007. A new class of bivariate distribution and its mixture. Journal of Multivariate Analysis 98, 1508–1527] introduced a new bivariate distribution using generalized exponential and exponential distributions. They discussed several interesting properties of this new distribution. Unfortunately, they did not discuss any estimation procedure of the unknown parameters. In this paper using the similar idea as of Sarhan and Balakrishnan [2007. A new class of bivariate distribution and its mixture. Journal of Multivariate Analysis 98, 1508–1527], we have proposed a singular bivariate distribution, which has an extra shape parameter. It is observed that the marginal distributions of the proposed bivariate distribution are more flexible than the corresponding marginal distributions of the Marshall–Olkin bivariate exponential distribution, Sarhan–Balakrishnan's bivariate distribution or the bivariate generalized exponential distribution. Different properties of this new distribution have been discussed. We provide the maximum likelihood estimators of the unknown parameters using EM algorithm. We reported some simulation results and performed two data analysis for illustrative purposes. Finally we propose some generalizations of this bivariate model.

The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.

Marshall–Olkin semi-Burr and Marshall–Olkin Burr distributions are introduced and studied. Their various characteristics in
reliability analysis are derived. Applications in time series analysis are discussed.

The life lengths of the units in a system can be modelled by a bivariate distribution. In this paper, we suppose that the
joint distribution of the units is a symmetric bivariate Pareto (Lomax) distribution. For this model, we obtain basic reliability
properties for series and parallel systems.

In this paper, an efficient approach to search for the global threshold of image using Gaussian mixture model is proposed. Firstly, a gray-level histogram of an image is represented as a function of the frequencies of gray-level. Then to fit the Gaussian mixtures to the histogram of image, the expectation maximization (EM) algorithm is developed to estimate the number of Gaussian mixture of such histograms and their corresponding parameterization. Finally, the optimal threshold which is the average of these Gaussian mixture means is chosen. And the experimental results show that the new algorithm performs better.

Recently, classifier ensemble methods are gaining more and more attention in the machine-learning and data-mining communities. In most cases, the performance of an ensemble is better than a single classifier. Many methods for creating diverse classifiers were developed during the past decade. When these diverse classifiers are generated, it is important to select the proper base classifier to join the ensemble. Usually, this selection process is called pruning the ensemble. In general, the ensemble pruning is a selection process in which an optimal combination will be selected from many existing base classifiers. Some base classifiers containing useful information may be excluded in this pruning process. To avoid this problem, the multilayer ensemble pruning model is used in this paper. In this model, the pruning of one layer can be seen as a multimodal optimization problem. A novel multi-sub-swarm particle swarm optimization (MSSPSO) is used here to find multi-solutions for this multilayer ensemble pruning model. In this model, each base classifier will generate an oracle output. Each layer will use MSSPSO algorithm to generate a different pruning based on previous oracle output. A series of experiments using UCI dataset is conducted, the experimental results show that the multilayer ensemble pruning via MSSPSO algorithm can improve the generalization performance of the multi-classifiers ensemble system. Besides, the experimental results show a relationship between the diversity and the pruning technique.
Keywords: Particle swarm optimization; ensemble pruning; classifier ensemble; multi-layer ensemble model

A class of generalized bivariate Marshall–Olkin distributions, which includes as special cases the Marshall–Olkin bivariate exponential distribution and the Marshall–Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with properties related to evolution of dependence along time, are investigated for this class of distributions. Extensions of results previously presented in the literature are provided as well.

DOI: 10.1007/11427469_165 Several artificial neural network (ANN) models with a feed-forward, back-propagation network structure and various training algorithms, are developed to forecast daily and monthly river flow discharges in Manwan Reservoir. In order to test the applicability of these models, they are compared with a conventional time series flow prediction model. Results indicate that the ANN models provide better accuracy in forecasting river flow than does the auto-regression time series model. In particular, the scaled conjugate gradient algorithm furnishes the highest correlation coefficient and the smallest root mean square error. This ANN model is finally employed in the advanced water resource project of Yunnan Power Group. Author name used in this publication: Kwokwing Chau

DOI: 10.1016/j.autcon.2006.11.008 It is generally acknowledged that construction claims are highly complicated and are interrelated with a multitude of factors. It will be advantageous if the parties to a dispute have some insights to some degree of certainty how the case would be resolved prior to the litigation process. By its nature, the use of artificial neural networks (ANN) can be a cost-effective technique to help to predict the outcome of construction claims, provided with characteristics of cases and the corresponding past court decisions. This paper presents the adoption of a particle swarm optimization (PSO) model to train perceptrons in predicting the outcome of construction claims in Hong Kong. It is illustrated that the successful prediction rate of PSO-based network is up to 80%. Moreover, it is capable of producing faster and more accurate results than its counterparts of a benchmarking back-propagation ANN. This will furnish an alternative in assessing whether or not to take the case to litigation. Author name used in this publication: K. W. Chau

In this paper we show that the Marshall-Olkin extended Weibull distribution can be obtained as a compound distribution with mixing exponential distribution. In addition, we provide simple sufficient conditions for the shape of the hazard rate function of the distribution. Moreover, we extend the considered distribution to accommodate randomly right censored data. Finally, application of the extended distribution to a data set representing the remission times of bladder cancer patients is given and its goodness-of-fit is demonstrated.

We consider a generalization of the bivariate Farlie-Gumbel-Morgenstern (FGM) distribution by introducing additional parameters. For the generalized FGM distribution, the admissible range of the association parameter allowing positive quadrant dependence property is shown. Distributional properties of concomitants for this generalized FGM distribution are studied. Recurrence relations between moments of concomitants are presented.

Extendibility of Marshall-Olkin distributions via Lévy subordinators and an application to portfolio credit risk, Short summary of dissertation at the Technische Universität München

- J F Mai

J.F. Mai, Extendibility of Marshall-Olkin distributions via Lévy subordinators and an application to portfolio credit risk, Short summary of dissertation
at the Technische Universität München, 2010.