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Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew 基于II型滤波和巴塞洛缪抽样方案的陈分布可靠性特性估计与检验方法
Statistics, optimization & information computing Pub Date : 2020-12-07 DOI: 10.19139/SOIC-2310-5070-1032
A. Chaturvedi, Surinder Kumar
{"title":"Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew","authors":"A. Chaturvedi, Surinder Kumar","doi":"10.19139/SOIC-2310-5070-1032","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-1032","url":null,"abstract":"In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ, hazard rate h(t) and the two measures of reliability, namely R(t) = P (X > t), where X denotes the lifetime of an item and P = P (X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew. We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average confiddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"99-122"},"PeriodicalIF":0.0,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41911218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
GMM Estimation of Continuous-Time Bilinear Processes 连续双线性过程的GMM估计
Statistics, optimization & information computing Pub Date : 2020-10-08 DOI: 10.19139/soic-2310-5070-902
A. Bibi, F. Merahi
{"title":"GMM Estimation of Continuous-Time Bilinear Processes","authors":"A. Bibi, F. Merahi","doi":"10.19139/soic-2310-5070-902","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-902","url":null,"abstract":"This paper examines the moments properties in frequency domain of the class of \u0085first order continuous-timebilinear processes (COBL(1,1) for short) with time-varying (resp. time-invariant) coefficients. So, we used theassociated evolutionary (or time-varying) transfer functions to study the structure of second-order of the process and its powers. In particular, for time-invariant case, an expression of the moments of any order are showed and the continuous-time AR (CAR) representation of COBL(1,1) is given as well as some moments properties of special cases. Based on these results we are able to estimate the unknown parameters involved in model via the so-called generalized method of moments (GMM) illustrated by a Monte Carlo study and applied to modelling two foreign exchange rates of Algerian Dinar against U.S-Dollar (USD/DZD) and against the single European currency Euro (EUR/DZD).","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84575615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Family of Hybrid Conjugate Gradient Methods for Unconstrained Optimization 一类新的无约束优化混合共轭梯度方法
Statistics, optimization & information computing Pub Date : 2020-10-08 DOI: 10.19139/SOIC-2310-5070-480
O. J. Adeleke, A. Ezugwu, I. Osinuga
{"title":"A New Family of Hybrid Conjugate Gradient Methods for Unconstrained Optimization","authors":"O. J. Adeleke, A. Ezugwu, I. Osinuga","doi":"10.19139/SOIC-2310-5070-480","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-480","url":null,"abstract":"The conjugate gradient method is a very efficient iterative technique for solving large-scale unconstrained optimization problems. Motivated by recent modifications of some variants of the method and construction of hybrid methods, this study proposed four hybrid methods that are globally convergent as well as computationally efficient. The approach adopted for constructing the hybrid methods entails projecting ten recently modified conjugate gradient methods. Each of the hybrid methods is shown to satisfy the descent property independent of any line search technique and globally convergent under the influence of strong Wolfe line search. Results obtained from numerical implementation of these methods and performance profiling show that the methods are very competitive with well-known traditional methods.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"399-417"},"PeriodicalIF":0.0,"publicationDate":"2020-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42127883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors 序批式生物反应器优化控制的几何方法
Statistics, optimization & information computing Pub Date : 2020-09-26 DOI: 10.19139/SOIC-2310-5070-868
Nahla Abdellatif, Walid Bouhafs, J. Harmand, F. Jean
{"title":"A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors","authors":"Nahla Abdellatif, Walid Bouhafs, J. Harmand, F. Jean","doi":"10.19139/SOIC-2310-5070-868","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-868","url":null,"abstract":"In this work, we consider an optimal control problem of a biological sequencing batch reactor (SBR) for the treatment of pollutants in wastewater. This model includes two biological reactions, one being aerobic while the other is anoxic. The objective is to find an optimal oxygen-injecting strategy to reach, in minimal time and in a minimal time/energy compromise, a target where the pollutants concentrations must fulfill normative constraints. Using a geometrical approach, we solve a more general optimal control problem and thanks to Pontryagin’s Maximum Principle, we explicitly give the complete optimal strategy.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"368-382"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42149122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Topp-Leone odd log-logistic Gumbel Distribution: Properties and Applications Topp-Leone奇对数-logistic甘贝尔分布:性质及应用
Statistics, optimization & information computing Pub Date : 2020-09-26 DOI: 10.19139/SOIC-2310-5070-903
Fazlollah Lak, M. Alizadeh, H. Karamikabir
{"title":"The Topp-Leone odd log-logistic Gumbel Distribution: Properties and Applications","authors":"Fazlollah Lak, M. Alizadeh, H. Karamikabir","doi":"10.19139/SOIC-2310-5070-903","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-903","url":null,"abstract":"In this article, the Topp-Leone odd log-logistic Gumbel (TLOLL-Gumbel) family of distribution have beenstudied. This family, contains the very flexible skewed density function. We study many aspects of the new model like hazard rate function, asymptotics, useful expansions, moments, generating Function, R´enyi entropy and order statistics. We discuss maximum likelihood estimation of the model parameters. Further, we study flexibility of the proposed family are illustrated of two real data sets.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"288-310"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47299889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions 二阶半拟、半拟锥凸函数的非光滑向量优化问题
Statistics, optimization & information computing Pub Date : 2020-09-26 DOI: 10.19139/SOIC-2310-5070-839
S. Sharma, Priyanka Yadav
{"title":"Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions","authors":"S. Sharma, Priyanka Yadav","doi":"10.19139/SOIC-2310-5070-839","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-839","url":null,"abstract":"Recently, Suneja et al. [26] introduced new classes of second-order cone-(η, ξ)-convex functions along with their generalizations and used them to prove second-order Karush–Kuhn–Tucker (KKT) type optimality conditions and duality results for the vector optimization problem involving first-order differentiable and second-order directionally differentiable functions. In this paper, we move one step ahead and study a nonsmooth vector optimization problem wherein the functions involved are first and second-order directionally differentiable. We introduce new classes of nonsmooth second-order cone-semipseudoconvex and nonsmooth second-order cone-semiquasiconvex functions in terms of second-order directional derivatives. Second-order KKT type sufficient optimality conditions and duality results for the same problem are proved using these functions.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"383-398"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45415916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Simulation Study of Semiparametric Estimation in Copula Models Based on Minimum Alpha-Divergence 基于最小散度的Copula模型半参数估计仿真研究
Statistics, optimization & information computing Pub Date : 2020-09-11 DOI: 10.19139/soic-2310-5070-974
M. Mohammadi, M. Amini, M. Emadi
{"title":"A Simulation Study of Semiparametric Estimation in Copula Models Based on Minimum Alpha-Divergence","authors":"M. Mohammadi, M. Amini, M. Emadi","doi":"10.19139/soic-2310-5070-974","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-974","url":null,"abstract":"The purpose of this paper is to introduce two semiparametric methods for the estimation of copula parameter. These methods are based on minimum Alpha-Divergence between a non-parametric estimation of copula density using local likelihood probit transformation method and a true copula density function. A Monte Carlo study is performed to measure the performance of these methods based on Hellinger distance and Neyman divergence as special cases of Alpha-Divergence. Simulation results are compared to the Maximum Pseudo-Likelihood (MPL) estimation as a conventional estimation method in well-known bivariate copula models. These results show that the proposed method based on Minimum Pseudo Hellinger Distance estimation has a good performance in small sample size and weak dependency situations. The parameter estimation methods are applied to a real data set in Hydrology.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"457 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86865153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Convergence Analysis of a Stochastic Progressive Hedging Algorithm for Stochastic Programming 随机规划中一种随机递进套期保值算法的收敛性分析
Statistics, optimization & information computing Pub Date : 2020-08-06 DOI: 10.19139/soic-2310-5070-964
Zhenguo Mu, Junfeng Yang
{"title":"Convergence Analysis of a Stochastic Progressive Hedging Algorithm for Stochastic Programming","authors":"Zhenguo Mu, Junfeng Yang","doi":"10.19139/soic-2310-5070-964","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-964","url":null,"abstract":"Stochastic programming is an approach for solving optimization problems with uncertain data whose probability distribution is assumed to be known, and progressive hedging algorithm (PHA) is a well-known decomposition method for solving the underlying model. However, the per iteration computation of PHA could be very costly since it solves a large number of subproblems corresponding to all the scenarios. In this paper, a stochastic variant of PHA is studied. At each iteration, only a small fraction of the scenarios are selected uniformly at random and the corresponding variable components are updated accordingly, while the variable components corresponding to those not selected scenarios are kept untouch. Therefore, the per iteration cost can be controlled freely to achieve very fast iterations. We show that, though the per iteration cost is reduced significantly, the proposed stochastic PHA converges in an ergodic sense at the same sublinear rate as the original PHA.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"656-667"},"PeriodicalIF":0.0,"publicationDate":"2020-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47104166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Volatility Modelling of the BRICS Stock Markets 金砖国家股票市场的波动性模型
Statistics, optimization & information computing Pub Date : 2020-07-25 DOI: 10.19139/soic-2310-5070-977
Rosinah M Mukhodobwane, C. Sigauke, Wilbert Chagwiza, W. Garira
{"title":"Volatility Modelling of the BRICS Stock Markets","authors":"Rosinah M Mukhodobwane, C. Sigauke, Wilbert Chagwiza, W. Garira","doi":"10.19139/soic-2310-5070-977","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-977","url":null,"abstract":"Volatility modelling is a key factor in equity markets for risk and portfolio management. This paper focuses on the use of a univariate generalized autoregressive conditional heteroscedasticity (GARCH) models for modelling volatility of the BRICS (Brazil, Russia, India, China and South Africa) stock markets. The study extends the literature by conducting the volatility modelling under the assumptions of seven error distributions that include the normal, skewed-normal, Student’s t, skewed-Student’s t, generalized error distribution (GED), skewed-GED and the generalized hyperbolic (GHYP) distribution. It was observed that using an ARMA(1, 1)-GARCH(1, 1) model, volatilities of the Brazilian Bovespa and the Russian IMOEX markets can both be well characterized (or described) by a heavy-tailed Student’s t distribution, while the Indian NIFTY market’s volatility is best characterized by the generalized hyperbolic (GHYP) distribution. Also, the Chinese SHCOMP and South African JALSH markets’ volatilities are best described by the skew-GED and skew-Student’s t distribution, respectively. The study further observed that the persistence of volatility in the BRICS markets does not follow the same hierarchical pattern under the error distributions, except under the skew-Student’s t and GHYP distributions where the pattern is the same. Under these two assumptions, i.e. the skew-Student’s t and GHYP, in a descending hierarchical order of magnitudes, volatility with persistence is highest in the Chinese market, followed by the South African market, then the Russian, Indian and Brazilian markets, respectively. However, under each of the five non-Gaussian error distributions, the Chinese market is the most volatile, while the least volatile is the Brazilian market.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"749-772"},"PeriodicalIF":0.0,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49626119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Sample Paths Properties of Stochastic Processes from Orlicz Spaces, with Applications to Partial Differential Equations Orlicz空间随机过程的样本路径性质及其在偏微分方程中的应用
Statistics, optimization & information computing Pub Date : 2020-07-25 DOI: 10.19139/soic-2310-5070-880
L. Sakhno, Y. Kozachenko, E. Orsingher, O. Hopkalo
{"title":"Sample Paths Properties of Stochastic Processes from Orlicz Spaces, with Applications to Partial Differential Equations","authors":"L. Sakhno, Y. Kozachenko, E. Orsingher, O. Hopkalo","doi":"10.19139/soic-2310-5070-880","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-880","url":null,"abstract":"In this paper we obtain conditions for stochastic processes from Orlicz spaces defined on unbounded domains to have almost sure bounded and continuous sample paths. Estimates for distributions of suprema of the processes are presented. Conditions are given in terms of entropy integrals and majorant characteristics of Orlicz spaces. Possible applications to solutions of partial differential equations are discussed. Examples of processes are given for which the conditions of the main results are satisfied.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"722-739"},"PeriodicalIF":0.0,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45055760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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