Pub Date : 2020-12-08DOI: 10.19139/soic-2310-5070-1034
Rekha, Vikas Kumar
In this paper, we proposed a quantile version of cumulative Renyi entropy for residual and past lifetimes and study their properties. We also study quantile-based cumulative Renyi entropy for extreme order statistic when random variable untruncated or truncated in nature. Some characterization results are studied using the relationship between proposed information measure and reliability measure. We also examine it in relation to some applied problems such as weighted and equillibrium models.
{"title":"Study of Quantile-Based Cumulative Renyi Information Measure","authors":"Rekha, Vikas Kumar","doi":"10.19139/soic-2310-5070-1034","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-1034","url":null,"abstract":"In this paper, we proposed a quantile version of cumulative Renyi entropy for residual and past lifetimes and study their properties. We also study quantile-based cumulative Renyi entropy for extreme order statistic when random variable untruncated or truncated in nature. Some characterization results are studied using the relationship between proposed information measure and reliability measure. We also examine it in relation to some applied problems such as weighted and equillibrium models.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74996981","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}
Pub Date : 2020-12-07DOI: 10.19139/SOIC-2310-5070-1032
A. Chaturvedi, Surinder Kumar
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.
本文考虑Chen分布，导出了参数λ、危险率h(t)和可靠性的两个度量的umvue和mle，即R(t) = P (X > t)，其中X表示物品的寿命，P = P (X > Y)表示随机强度X的物品或系统在随机应力Y作用下的可靠性，在II型审查方案和Bartholomew抽样方案下。我们还开发了可靠性度量的区间估计。测试程序的假设相关的不同参数函数也已开发。通过仿真研究，对不同的点估计方法和平均置信长度进行了比较研究。为了说明目的，给出了一个真实数据集的分析。
{"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}
Pub Date : 2020-10-08DOI: 10.19139/soic-2310-5070-902
A. Bibi, F. Merahi
This paper examines the moments properties in frequency domain of the class of first 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).
{"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}
Pub Date : 2020-10-08DOI: 10.19139/SOIC-2310-5070-480
O. J. Adeleke, A. Ezugwu, I. Osinuga
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.
{"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}
Pub Date : 2020-09-26DOI: 10.19139/SOIC-2310-5070-868
Nahla Abdellatif, Walid Bouhafs, J. Harmand, F. Jean
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.
{"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}
Pub Date : 2020-09-26DOI: 10.19139/SOIC-2310-5070-903
Fazlollah Lak, M. Alizadeh, H. Karamikabir
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.
{"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}
Pub Date : 2020-09-26DOI: 10.19139/SOIC-2310-5070-839
S. Sharma, Priyanka Yadav
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.
最近，Suneja et al.[26]引入了一类新的二阶锥-(η， ξ)-凸函数及其推广，并利用它们证明了二阶Karush-Kuhn-Tucker (KKT)型最优性条件和对偶性结果，该问题涉及一阶可微函数和二阶方向可微函数。在本文中，我们进一步研究了一个非光滑向量优化问题，其中所涉及的函数是一阶和二阶方向可微的。从二阶方向导数的角度引入了一类新的非光滑二阶锥-半拟凸函数和非光滑二阶锥-半拟凸函数。利用这些函数证明了同一问题的二阶KKT型充分最优性条件和对偶性结果。
{"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}
Pub Date : 2020-09-11DOI: 10.19139/soic-2310-5070-974
M. Mohammadi, M. Amini, M. Emadi
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.
{"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}
Pub Date : 2020-08-06DOI: 10.19139/soic-2310-5070-964
Zhenguo Mu, Junfeng Yang
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.
{"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}
Pub Date : 2020-07-25DOI: 10.19139/soic-2310-5070-880
L. Sakhno, Y. Kozachenko, E. Orsingher, O. Hopkalo
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.
{"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}
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