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Sampling theorem and efficiency comparison of three local minimum variance unbiased estimators of the mean and variance of the exponential distribution 指数分布均值和方差的三种局部最小方差无偏估计的抽样定理和效率比较
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1492886
Guoan Li, Muzhen Li
{"title":"Sampling theorem and efficiency comparison of three local minimum variance unbiased estimators of the mean and variance of the exponential distribution","authors":"Guoan Li, Muzhen Li","doi":"10.1080/25742558.2018.1492886","DOIUrl":"https://doi.org/10.1080/25742558.2018.1492886","url":null,"abstract":"Abstract This article continues the works of references to improve and perfect the sampling theorem of exponential distribution. First, the distribution of the sample range of exponential distribution is derived, and that the sample range is mutually independent of the sample minimum is proven. Then, this article derives the distribution of the difference between sample maximum and mean and demonstrates that the difference of these two statistics is mutually independent of the sample minimum. Thus, three local minimum variance unbiased estimators of the mean could be constructed. The estimator built by sample minimum and the difference between sample mean and minimum is precisely the uniformly minimum-variance unbiased estimator (UMVUE) of the mean. Similarly, three local minimum variance unbiased estimators of the variance are derived. At last, the efficiency comparison is made among the above three local minimum variance unbiased estimators of mean and variance of the exponential distribution.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1492886","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44072597","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
Improved inference for the panel data model with unknown unit-specific heteroscedasticity: A Monte Carlo evidence 具有未知单位特异性异方差的面板数据模型的改进推断:蒙特卡罗证据
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1463598
Afshan Saeed, M. Aslam, Saima Altaf, M. Amanullah
{"title":"Improved inference for the panel data model with unknown unit-specific heteroscedasticity: A Monte Carlo evidence","authors":"Afshan Saeed, M. Aslam, Saima Altaf, M. Amanullah","doi":"10.1080/25742558.2018.1463598","DOIUrl":"https://doi.org/10.1080/25742558.2018.1463598","url":null,"abstract":"Abstract For a panel data model (PDM), it is common that the error terms of panel regression model are heteroscedastic. In the available literature, the heteroscedastic consistent covariance matrix estimators (HCCMEs) have been used for adequate testing of the coefficients of PDM. Usually, these HCCMEs are based on the residuals derived from ordinary least square (OLS) estimator which is considerably inefficient in the presence of heteroscedasticity. To get efficient estimation, the existing literature proposes some adaptive estimators for the PDM. This paper presents the HCCMEs, derived from some adaptive estimator, while considering the panel data-set with unit-specific heteroscedasticity. Through the Monte Carlo simulations, we present the numerical evaluation and attractive findings.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1463598","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43527815","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
Fixed points of rational type contractions in G-metric spaces G-度量空间中有理型收缩的不动点
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/23311835.2018.1444904
Yaé Ulrich Gaba
{"title":"Fixed points of rational type contractions in G-metric spaces","authors":"Yaé Ulrich Gaba","doi":"10.1080/23311835.2018.1444904","DOIUrl":"https://doi.org/10.1080/23311835.2018.1444904","url":null,"abstract":"We establish three major fixed-point theorems for functions satisfying generalized rational type almost contraction conditions. Firstly we consider the case of a single mapping, secondly we look at the case of a triplet of mappings and we conclude by the case of a family of mappings. The theorems we present generalize similar results already obtained by Abbas, Rhoades, Gaba, and others. The operators we consider are all of the weakly Picard type.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1444904","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49382375","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
Fractional dynamic inequalities harmonized on time scales 在时间尺度上协调的分数动态不等式
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/23311835.2018.1438030
Muhammad Jibril Shahab Sahir
{"title":"Fractional dynamic inequalities harmonized on time scales","authors":"Muhammad Jibril Shahab Sahir","doi":"10.1080/23311835.2018.1438030","DOIUrl":"https://doi.org/10.1080/23311835.2018.1438030","url":null,"abstract":"Abstract We present here some symmetric fractional Rogers-Hölder’s inequalities using Riemann–Liouville integral on time scales. We consider and impose different conditions on three non-zero real numbers p, q and r when .","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1438030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60067349","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 whale optimization algorithm (WOA) approach for clustering 一种用于聚类的鲸鱼优化算法（WOA）
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1483565
J. Nasiri, F. M. Khiyabani
{"title":"A whale optimization algorithm (WOA) approach for clustering","authors":"J. Nasiri, F. M. Khiyabani","doi":"10.1080/25742558.2018.1483565","DOIUrl":"https://doi.org/10.1080/25742558.2018.1483565","url":null,"abstract":"Abstract Clustering is a powerful technique in data-mining, which involves identifing homogeneous groups of objects based on the values of attributes. Meta-heuristic algorithms such as particle swarm optimization, artificial bee colony, genetic algorithm and differential evolution are now becoming powerful methods for clustering. In this paper, we propose a new meta-heuristic clustering method, the Whale Clustering Optimization Algorithm, based on the swarm foraging behavior of humpback whales. After a detailed formulation and explanation of its implementation, we will then compare the proposed algorithm with other existing well-known algorithms in clustering, including PSO, ABC, GA, DE and k-means. Proposed algorithm was tested using one artificial and seven real benchmark data sets from the UCI machine learning repository. Simulations show that the proposed algorithm can successfully be used for data clustering.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1483565","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46976803","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: 146
A space-fractional-reaction-diffusion model for pattern formation in coral reefs 珊瑚礁模式形成的空间分数反应扩散模型
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/23311835.2018.1426524
L. Somathilake, K. Burrage
{"title":"A space-fractional-reaction-diffusion model for pattern formation in coral reefs","authors":"L. Somathilake, K. Burrage","doi":"10.1080/23311835.2018.1426524","DOIUrl":"https://doi.org/10.1080/23311835.2018.1426524","url":null,"abstract":"In this paper, we propose a Space Fractional Reaction-Diffusion model for growth of corals in a tank. We analyse spatial temporal pattern formation behavior of the model through Turing type instability analysis. We determine the parameter regions of the model, in which the Turing instability occurs (the Turing instability space). We then discuss the effects of the fractional order and the model parameters on the spatial temporal patterns of the model. We investigate numerical solutions of the model using the Fourier Spectral method, two Euler type schemes and the MATLAB functionODE15s. The main advantage of using the Fourier spectral method is ability to represent the space fractional operator in fully diagonal form and ability to extend straightforwardly to two and three spatial dimensions. To find the numerical solutions with the other three methods, we transform the model equations into a system of ODEs by applying Matrix Transfer Technique and solve those system of ODEs. We compare the numerical solutions obtained by these methods and efficiencies of these methods.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1426524","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46978738","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: 9
A micro-macro hybrid model with application for material and pedestrian flow 一种具有应用价值的材料流和人流微观-宏观混合模型
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1476049
S. Göttlich, Marion Pfirsching
{"title":"A micro-macro hybrid model with application for material and pedestrian flow","authors":"S. Göttlich, Marion Pfirsching","doi":"10.1080/25742558.2018.1476049","DOIUrl":"https://doi.org/10.1080/25742558.2018.1476049","url":null,"abstract":"Abstract In this paper, a hybrid modeling approach for granular flow-like applications is presented. The approach allows to switch for a priori fixed points in time between the different levels of description which are the microscopic and macroscopic scale, respectively. Based on the numerical discretization of the models, the switching procedure is able to interpret information on individual objects as density distributions and vice versa. In particular, the reverse direction, i.e. from a macroscopic to a microscopic perspective, requires the solution of a nonlinear least squares problem subject to further constraints. Simulation results are given and demonstrate the good performance of the algorithm in the case of material and pedestrian flow models.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1476049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47841627","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: 4
An improved generalized class of estimators for population variance using auxiliary variables 一类使用辅助变量的改进广义总体方差估计量
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1454579
N. K. Adichwal, Jitendra Kumar, Rajesh Singh
{"title":"An improved generalized class of estimators for population variance using auxiliary variables","authors":"N. K. Adichwal, Jitendra Kumar, Rajesh Singh","doi":"10.1080/25742558.2018.1454579","DOIUrl":"https://doi.org/10.1080/25742558.2018.1454579","url":null,"abstract":"Abstract This paper proposed an improved generalized class of estimator for estimating population variance using auxiliary variables based on simple random sampling without replacement. The expression of mean square error of the proposed estimator is obtained up to the first order of approximation. We have derived the conditions for the parameters under which the proposed estimator performs better compared to the usual estimator and other existing estimators. An empirical study and simulation study are also carried out with the support of theoretical results.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1454579","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43722714","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
On generalizations of classical primary submodules over commutative rings 交换环上经典初等子模的推广
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1458556
P. Yiarayong, M. 
{"title":"On generalizations of classical primary submodules over commutative rings","authors":"P. Yiarayong, M. ","doi":"10.1080/25742558.2018.1458556","DOIUrl":"https://doi.org/10.1080/25742558.2018.1458556","url":null,"abstract":"Abstract Let be a function where is the set of all submodules of R-module M. A proper submodule N of M is called a ϕ-classical primary submodule, if for each m ∊ M and a, b ∊ R with abm ∊ N-ϕ(N), then am ∊ N or bnm ∊ N for some positive integer n. Some characterizations of classical primary and ϕ-classical primary submodules are obtained. It is shown that N is a ϕ-classical primary submodule of M if and only if for every m ∊ M−N, (N:m) is a φ-primary ideal of R where (ϕ(N):m) = φ(N:m). Moreover, we investigate relationships between classical primary, ϕ-classical primary and ϕ-primary submodules of modules over commutative rings. Finally, we obtain necessary and sufficient conditions of a ϕ-classical primary submodule in order to be a ϕ-primary submodule.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1458556","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47781061","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
Functions and wν-Lindelöf with respect to a hereditary class 关于一个遗传类的函数和wΓ-Lindelöf
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1479218
Mariam Abuage, A. Kılıçman
{"title":"Functions and wν-Lindelöf with respect to a hereditary class","authors":"Mariam Abuage, A. Kılıçman","doi":"10.1080/25742558.2018.1479218","DOIUrl":"https://doi.org/10.1080/25742558.2018.1479218","url":null,"abstract":"Abstract A collection of a nonempty subsets of is called hereditary class if it is closed under hereditary property. In this work, we define and study the notion of some generalizations of -Lindelöf generalized topological spaces with respect to a hereditary class, namely; -Lindelöf hereditary generalized topological spaces. Moreover, investigate basic properties of the concepts, its relation to known concepts and its preservation by functions properties.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1479218","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45463832","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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