Pub Date : 2021-08-06DOI: 10.1108/ajms-04-2021-0083
M. López-García
PurposeIn this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+.Design/methodology/approachThe author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace.FindingsThe author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones.Originality/valueThe author computes the Hilbert transform of powers of |lnx| to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform.
{"title":"Operators on the vanishing moments subspace and Stieltjes classes for M-indeterminate probability distributions","authors":"M. López-García","doi":"10.1108/ajms-04-2021-0083","DOIUrl":"https://doi.org/10.1108/ajms-04-2021-0083","url":null,"abstract":"PurposeIn this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+.Design/methodology/approachThe author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace.FindingsThe author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones.Originality/valueThe author computes the Hilbert transform of powers of |lnx| to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47871504","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 : 2021-07-14DOI: 10.1108/AJMS-02-2021-0037
G. A. Okeke, Daniel Francis
PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.Research limitations/implicationsAnalytical and theoretical results.Practical implicationsThe results of this paper can be applied in science and engineering.Social implicationsThe results of this paper is applicable in certain social sciences.Originality/valueThe results of this paper are new and will open up new areas of research in mathematical sciences.
{"title":"Some fixed-point theorems for a general class of mappings in modular G-metric spaces","authors":"G. A. Okeke, Daniel Francis","doi":"10.1108/AJMS-02-2021-0037","DOIUrl":"https://doi.org/10.1108/AJMS-02-2021-0037","url":null,"abstract":"PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.Research limitations/implicationsAnalytical and theoretical results.Practical implicationsThe results of this paper can be applied in science and engineering.Social implicationsThe results of this paper is applicable in certain social sciences.Originality/valueThe results of this paper are new and will open up new areas of research in mathematical sciences.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44106123","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 : 2021-07-14DOI: 10.1108/AJMS-01-2021-0025
Jihane Abdelli, B. Brahimi
PurposeIn this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its properties, effectiveness, flexibility and reliability of the nonparametric methods, which have limiting chi-square distributions and may be used to obtain tests or confidence intervals. The authors derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Design/methodology/approachIn this paper we applied the empirical likelihood method which originally proposed by Owen, to the copula moment based estimation methods.FindingsWe derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Originality/valueIn this paper we applied the empirical likelihood method which originally proposed by Owen 1988, to the copula moment based estimation methods given by Brahimi and Necir 2012. We derive an new estimator of copula parameters and the asymptotic normality of the empirical likelihood based on copula moment estimation methods.
{"title":"On copula moment: empirical likelihood based estimation method","authors":"Jihane Abdelli, B. Brahimi","doi":"10.1108/AJMS-01-2021-0025","DOIUrl":"https://doi.org/10.1108/AJMS-01-2021-0025","url":null,"abstract":"PurposeIn this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its properties, effectiveness, flexibility and reliability of the nonparametric methods, which have limiting chi-square distributions and may be used to obtain tests or confidence intervals. The authors derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Design/methodology/approachIn this paper we applied the empirical likelihood method which originally proposed by Owen, to the copula moment based estimation methods.FindingsWe derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Originality/valueIn this paper we applied the empirical likelihood method which originally proposed by Owen 1988, to the copula moment based estimation methods given by Brahimi and Necir 2012. We derive an new estimator of copula parameters and the asymptotic normality of the empirical likelihood based on copula moment estimation methods.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47515479","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 : 2021-07-06DOI: 10.1108/ajms-03-2021-0058
D. Dey, D. Mandal, M. Mukherjee
PurposeThe present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space.Design/methodology/approachThe existence of uniformity for a completely regular topological space is well-known, and the interrelation of this structure with a proximity is also well-studied. Using this idea, a structure on generalized topological space has been developed, to establish the same type of compatibility in the corresponding frameworks.FindingsIt is proved, among other things, that a μ-uniformity on a non-empty set X always induces a generalized topology on X, which is μ-completely regular too. In the last theorem of the paper, the authors develop a relation between μ-proximity and μ-uniformity by showing that every μ-uniformity generates a μ-proximity, both giving the same generalized topology on the underlying set.Originality/valueIt is an original work influenced by the previous works that have been done on generalized topological spaces. A kind of generalization has been done in this article, that has produced an intermediate structure to the already known generalized topological spaces.
{"title":"Uniformity on generalized topological spaces","authors":"D. Dey, D. Mandal, M. Mukherjee","doi":"10.1108/ajms-03-2021-0058","DOIUrl":"https://doi.org/10.1108/ajms-03-2021-0058","url":null,"abstract":"PurposeThe present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space.Design/methodology/approachThe existence of uniformity for a completely regular topological space is well-known, and the interrelation of this structure with a proximity is also well-studied. Using this idea, a structure on generalized topological space has been developed, to establish the same type of compatibility in the corresponding frameworks.FindingsIt is proved, among other things, that a μ-uniformity on a non-empty set X always induces a generalized topology on X, which is μ-completely regular too. In the last theorem of the paper, the authors develop a relation between μ-proximity and μ-uniformity by showing that every μ-uniformity generates a μ-proximity, both giving the same generalized topology on the underlying set.Originality/valueIt is an original work influenced by the previous works that have been done on generalized topological spaces. A kind of generalization has been done in this article, that has produced an intermediate structure to the already known generalized topological spaces.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46364362","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 : 2021-07-01DOI: 10.1108/AJMS-01-2021-0013
S. Nayaka, T. K. Sreelakshmi, Santosh Kumar
PurposeIn this paper, the author defines the function B¯i,jδ,k(n), the number of singular overpartition pairs of n without multiples of k in which no part is divisible by δ and only parts congruent to ± i, ± j modulo δ may be overlined.Design/methodology/approachAndrews introduced to combinatorial objects, which he called singular overpartitions and proved that these singular overpartitions depend on two parameters δ and i can be enumerated by the function C¯δ,i(n), which gives the number of overpartitions of n in which no part divisible by δ and parts ≡ ± i(Mod δ) may be overlined.FindingsUsing classical spirit of q-series techniques, the author obtains congruences modulo 4 for B¯2,48,3(n), B¯
{"title":"Arithmetic properties of singular overpartition pairs without multiples of k","authors":"S. Nayaka, T. K. Sreelakshmi, Santosh Kumar","doi":"10.1108/AJMS-01-2021-0013","DOIUrl":"https://doi.org/10.1108/AJMS-01-2021-0013","url":null,"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose</jats:title><jats:p>In this paper, the author defines the function <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:msubsup><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>B</m:mi></m:mrow><m:mo>¯</m:mo></m:mover></m:mrow><m:mrow><m:mi>i</m:mi><m:mo>,</m:mo><m:mi>j</m:mi></m:mrow><m:mrow><m:mi>δ</m:mi><m:mo>,</m:mo><m:mi>k</m:mi></m:mrow></m:msubsup><m:mrow><m:mo stretchy=\"false\">(</m:mo><m:mrow><m:mi>n</m:mi></m:mrow><m:mo stretchy=\"false\">)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2021-0013001.tif\" /></jats:inline-formula>, the number of singular overpartition pairs of <jats:italic>n</jats:italic> without multiples of <jats:italic>k</jats:italic> in which no part is divisible by <jats:italic>δ</jats:italic> and only parts congruent to ± <jats:italic>i</jats:italic>, ± <jats:italic>j</jats:italic> modulo <jats:italic>δ</jats:italic> may be overlined.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design/methodology/approach</jats:title><jats:p>Andrews introduced to combinatorial objects, which he called singular overpartitions and proved that these singular overpartitions depend on two parameters <jats:italic>δ</jats:italic> and <jats:italic>i</jats:italic> can be enumerated by the function <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:msub><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>C</m:mi></m:mrow><m:mo>¯</m:mo></m:mover></m:mrow><m:mrow><m:mi>δ</m:mi><m:mo>,</m:mo><m:mi>i</m:mi></m:mrow></m:msub><m:mrow><m:mo stretchy=\"false\">(</m:mo><m:mrow><m:mi>n</m:mi></m:mrow><m:mo stretchy=\"false\">)</m:mo></m:mrow></m:math>,<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2021-0013002.tif\" /></jats:inline-formula> which gives the number of overpartitions of <jats:italic>n</jats:italic> in which no part divisible by <jats:italic>δ</jats:italic> and parts ≡ ± <jats:italic>i</jats:italic>(Mod <jats:italic>δ</jats:italic>) may be overlined.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings</jats:title><jats:p>Using classical spirit of <jats:italic>q</jats:italic>-series techniques, the author obtains congruences modulo 4 for <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:msubsup><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>B</m:mi></m:mrow><m:mo>¯</m:mo></m:mover></m:mrow><m:mrow><m:mn>2,4</m:mn></m:mrow><m:mrow><m:mn>8,3</m:mn></m:mrow></m:msubsup><m:mrow><m:mo stretchy=\"false\">(</m:mo><m:mrow><m:mi>n</m:mi></m:mrow><m:mo stretchy=\"false\">)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2021-0013003.tif\" /></jats:inline-formula>, <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:msubsup><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>B</m:mi></m:mrow><m:mo>¯</","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46266869","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 : 2021-06-22DOI: 10.1108/ajms-12-2020-0126
Khadidja Addad, S. Ouakkas
PurposeIn this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ∇¯ in relation to those for ∇ and ∇^.Design/methodology/approachIn the first section of this paper, we prove some results about the α-connections of a statistical manifold where we give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds treated in [1, 3], and we construct some examples.FindingsWe give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.Originality/valueWe give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.
{"title":"On the α-connections and the α-conformal equivalence on statistical manifolds","authors":"Khadidja Addad, S. Ouakkas","doi":"10.1108/ajms-12-2020-0126","DOIUrl":"https://doi.org/10.1108/ajms-12-2020-0126","url":null,"abstract":"PurposeIn this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ∇¯ in relation to those for ∇ and ∇^.Design/methodology/approachIn the first section of this paper, we prove some results about the α-connections of a statistical manifold where we give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds treated in [1, 3], and we construct some examples.FindingsWe give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.Originality/valueWe give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48751672","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 : 2021-06-21DOI: 10.1108/ajms-02-2021-0052
M. Ali, Mohammed K Almoaeet, Basim Albuohimad
PurposeThis study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented.Design/methodology/approachIn this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox.FindingsApplying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations.Originality/valueThis paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain.
{"title":"Numerical simulation method of lines together with a pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative","authors":"M. Ali, Mohammed K Almoaeet, Basim Albuohimad","doi":"10.1108/ajms-02-2021-0052","DOIUrl":"https://doi.org/10.1108/ajms-02-2021-0052","url":null,"abstract":"PurposeThis study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented.Design/methodology/approachIn this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox.FindingsApplying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations.Originality/valueThis paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48387153","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 : 2021-06-02DOI: 10.1108/ajms-02-2022-0033
Saida Mancer, A. Necir, S. Benchaira
PurposeThe purpose of this paper is to propose a semiparametric estimator for the tail index of Pareto-type random truncated data that improves the existing ones in terms of mean square error. Moreover, we establish its consistency and asymptotic normality.Design/methodology/approachTo construct a root mean squared error (RMSE)-reduced estimator of the tail index, the authors used the semiparametric estimator of the underlying distribution function given by Wang (1989). This allows us to define the corresponding tail process and provide a weak approximation to this one. By means of a functional representation of the given estimator of the tail index and by using this weak approximation, the authors establish the asymptotic normality of the aforementioned RMSE-reduced estimator.FindingsIn basis on a semiparametric estimator of the underlying distribution function, the authors proposed a new estimation method to the tail index of Pareto-type distributions for randomly right-truncated data. Compared with the existing ones, this estimator behaves well both in terms of bias and RMSE. A useful weak approximation of the corresponding tail empirical process allowed us to establish both the consistency and asymptotic normality of the proposed estimator.Originality/valueA new tail semiparametric (empirical) process for truncated data is introduced, a new estimator for the tail index of Pareto-type truncated data is introduced and asymptotic normality of the proposed estimator is established.
{"title":"Semiparametric tail-index estimation for randomly right-truncated heavy-tailed data","authors":"Saida Mancer, A. Necir, S. Benchaira","doi":"10.1108/ajms-02-2022-0033","DOIUrl":"https://doi.org/10.1108/ajms-02-2022-0033","url":null,"abstract":"PurposeThe purpose of this paper is to propose a semiparametric estimator for the tail index of Pareto-type random truncated data that improves the existing ones in terms of mean square error. Moreover, we establish its consistency and asymptotic normality.Design/methodology/approachTo construct a root mean squared error (RMSE)-reduced estimator of the tail index, the authors used the semiparametric estimator of the underlying distribution function given by Wang (1989). This allows us to define the corresponding tail process and provide a weak approximation to this one. By means of a functional representation of the given estimator of the tail index and by using this weak approximation, the authors establish the asymptotic normality of the aforementioned RMSE-reduced estimator.FindingsIn basis on a semiparametric estimator of the underlying distribution function, the authors proposed a new estimation method to the tail index of Pareto-type distributions for randomly right-truncated data. Compared with the existing ones, this estimator behaves well both in terms of bias and RMSE. A useful weak approximation of the corresponding tail empirical process allowed us to establish both the consistency and asymptotic normality of the proposed estimator.Originality/valueA new tail semiparametric (empirical) process for truncated data is introduced, a new estimator for the tail index of Pareto-type truncated data is introduced and asymptotic normality of the proposed estimator is established.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45186382","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 : 2021-05-07DOI: 10.1108/AJMS-10-2020-0094
H. Kumara, V. Venkatesha
PurposeBesse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds.Design/methodology/approachThe paper opted the tensor calculus on manifolds to find the solution of the CPE.FindingsIn this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with lambda=tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting.Originality/valueThe paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.
{"title":"Critical point equation on almost f-cosymplectic manifolds","authors":"H. Kumara, V. Venkatesha","doi":"10.1108/AJMS-10-2020-0094","DOIUrl":"https://doi.org/10.1108/AJMS-10-2020-0094","url":null,"abstract":"PurposeBesse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds.Design/methodology/approachThe paper opted the tensor calculus on manifolds to find the solution of the CPE.FindingsIn this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with lambda=tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting.Originality/valueThe paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43265684","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 : 2021-05-03DOI: 10.1108/AJMS-11-2020-0125
L. Belarbi, H. Elhendi
PurposeLet (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature, scalar and sectional curvatures.Design/methodology/approachIn this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle.FindingsThe authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures.Originality/valueThe authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures.
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