The extremal convex bodies of constant width for the Minkowski measure of asymmetry are discussed. A result, similar to that of H. Groemer＇s and of H. Lu＇s, is obtained, which states that, for the Minkowski measure ...The extremal convex bodies of constant width for the Minkowski measure of asymmetry are discussed. A result, similar to that of H. Groemer＇s and of H. Lu＇s, is obtained, which states that, for the Minkowski measure of asymmetry, the most asymmetric convex domains of constant width in R2 are Reuleaux triangles.展开更多
Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continui...Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on （1, ＋∞） is confirmed, and the connections between general p-critical points and the Minkowski-critical points （∞-critical points） are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.展开更多
In this paper,the p-Minkowski type measures of asymmetry for convex bodies,which have the well-known Minkowski measure of asymmetry as the special case p=∞,are introduced,and some properties of the p-Minkowski type m...In this paper,the p-Minkowski type measures of asymmetry for convex bodies,which have the well-known Minkowski measure of asymmetry as the special case p=∞,are introduced,and some properties of the p-Minkowski type measures are investigated.展开更多
In this article,we highlight a new three-parameter heavy-tailed lifetime distribution that aims to extend the modeling possibilities of the Lomax distribution.It is called the extended Lomax distribution.The considere...In this article,we highlight a new three-parameter heavy-tailed lifetime distribution that aims to extend the modeling possibilities of the Lomax distribution.It is called the extended Lomax distribution.The considered distribution naturally appears as the distribution of a transformation of a random variable following the logweighted power distribution recently introduced for percentage or proportion data analysis purposes.As a result,its cumulative distribution has the same functional basis as that of the Lomax distribution,but with a novel special logarithmic term depending on several parameters.The modulation of this logarithmic term reveals new types of asymetrical shapes,implying a modeling horizon beyond that of the Lomax distribution.In the first part,we examine several of its mathematical properties,such as the shapes of the related probability and hazard rate functions;stochastic comparisons;manageable expansions for various moments;and quantile properties.In particular,based on the quantile functions,various actuarial measures are discussed.In the second part,the distribution’s applicability is investigated with the use of themaximumlikelihood estimationmethod.The behavior of the obtained parameter estimates is validated by a simulation work.Insurance claim data are analyzed.We show that the proposed distribution outperforms eight well-known distributions,including the Lomax distribution and several extended Lomax distributions.In addition,we demonstrate that it gives preferable inferences from these competitor distributions in terms of risk measures.展开更多
Recently, the connection between p-measures of asymmetry and the L_p-mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed insp...Recently, the connection between p-measures of asymmetry and the L_p-mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p-measures of asymmetry for star bodies（naturally for convex bodies） is introduced first. Then the connection between dual p-measures of asymmetry and Lp-dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.展开更多
The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-...The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced by Q.Guo.Then,a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R.J.Gardner,D.Hug and W.Weil recently,which is an extension of the p-measures.展开更多
基金The NSF (08KJD110016) of Jiangsu Hight Education
文摘The extremal convex bodies of constant width for the Minkowski measure of asymmetry are discussed. A result, similar to that of H. Groemer＇s and of H. Lu＇s, is obtained, which states that, for the Minkowski measure of asymmetry, the most asymmetric convex domains of constant width in R2 are Reuleaux triangles.
基金The NSF(11271282)of Chinathe GIF(CXLX12 0865)of Jiangsu Province
文摘Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on （1, ＋∞） is confirmed, and the connections between general p-critical points and the Minkowski-critical points （∞-critical points） are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.
基金Supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX20_2745)the National Natural Science Foundation of China(12071334 and 12071277)
文摘In this paper,the p-Minkowski type measures of asymmetry for convex bodies,which have the well-known Minkowski measure of asymmetry as the special case p=∞,are introduced,and some properties of the p-Minkowski type measures are investigated.
基金funded by the Deanship Scientific Research(DSR),King Abdulaziz University,Jeddah,under the GrantNo.KEP-PhD:21-130-1443.
文摘In this article,we highlight a new three-parameter heavy-tailed lifetime distribution that aims to extend the modeling possibilities of the Lomax distribution.It is called the extended Lomax distribution.The considered distribution naturally appears as the distribution of a transformation of a random variable following the logweighted power distribution recently introduced for percentage or proportion data analysis purposes.As a result,its cumulative distribution has the same functional basis as that of the Lomax distribution,but with a novel special logarithmic term depending on several parameters.The modulation of this logarithmic term reveals new types of asymetrical shapes,implying a modeling horizon beyond that of the Lomax distribution.In the first part,we examine several of its mathematical properties,such as the shapes of the related probability and hazard rate functions;stochastic comparisons;manageable expansions for various moments;and quantile properties.In particular,based on the quantile functions,various actuarial measures are discussed.In the second part,the distribution’s applicability is investigated with the use of themaximumlikelihood estimationmethod.The behavior of the obtained parameter estimates is validated by a simulation work.Insurance claim data are analyzed.We show that the proposed distribution outperforms eight well-known distributions,including the Lomax distribution and several extended Lomax distributions.In addition,we demonstrate that it gives preferable inferences from these competitor distributions in terms of risk measures.
基金Supported by the National Natural Science Foundation of China(12671293,11701118,U1201252)the National High Technology Research&Development Program of China(2015AA015408)the Special Fund for Science & Technology Platform and Talent Team Project of Guizhou Province(Qian KeHe Ping Tai RenCai [2016]5609)
文摘Recently, the connection between p-measures of asymmetry and the L_p-mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p-measures of asymmetry for star bodies（naturally for convex bodies） is introduced first. Then the connection between dual p-measures of asymmetry and Lp-dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271244 and 11271282)
文摘The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced by Q.Guo.Then,a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R.J.Gardner,D.Hug and W.Weil recently,which is an extension of the p-measures.
文摘目的 对辽宁地区骨性Ⅰ类女性下颌骨几何进行三维CT重建技术(3DCT),并利用欧几里得距离矩阵分析(EDMA)进行形态的不对称性分析,对口腔正畸方案的设计及法医牙科鉴定方向提供重要的形态学基础资料。方法 选取2020年7月至2021年7月沈阳市表型组学研究重点实验室影像数据库中的50名辽宁地区骨性Ⅰ类女性进行3D头部CT进行回顾性分析,将数据录入VG Studio 3.2 MAX进行下颌骨三维重建并测量标志点三维坐标,使用winEDMA Version 1.0.1软件对左右侧下颌骨标志点进行不对称性分析。结果 用bootstrap非参数统计检验法分析结果显示,t=1.164、P=0.001。25个形状差异矩阵比值中小于0.95的有5个(20%);>1.05的有0个。辽宁地区骨性Ⅰ类女性下颌骨左右形状差异有统计学意义。结论 辽宁地区骨性Ⅰ类女性下颌骨具有不对称性且右侧偏大。
