The objective of this article is to demonstrate with examples that the two-sided tie correction does not work well. This correction was developed by Cureton so that Kendall’s tau-type and Spearman’s rho-type formula...The objective of this article is to demonstrate with examples that the two-sided tie correction does not work well. This correction was developed by Cureton so that Kendall’s tau-type and Spearman’s rho-type formulas for rank-biserial correlation yield the same result when ties are present. However, a correction based on the bracket ties achieves the desired goal, which is demonstrated algebraically and checked with three examples. On the one hand, the 10-element random sample given by Cureton, in which the two-sided tie correction performs well, is taken up. On the other hand, two other examples are given, one with a 7-element random sample and the other with a clinical random sample of 31 participants, in which the two-sided tie correction does not work, but the new correction does. It is concluded that the new corrected formulas coincide with Goodman-Kruskal’s gamma as compared to Glass’ formula that matches Somers’ d<sub>Y</sub><sub>|X</sub> or asymmetric measure of association of Y ranking with respect to X dichotomy. The use of this underreported coefficient is suggested, which is very easy to calculate from its equivalence with Kruskal-Wallis’ gamma and Somers’ d<sub>Y</sub><sub>|X</sub>.展开更多
Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has...Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.展开更多
The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under lower moment conditions or the Lindeberg condition. Results obtained improve a central lim...The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under lower moment conditions or the Lindeberg condition. Results obtained improve a central limit theorem of Roussas[11]for negatively associated fields and the main results of Su and Chi [18]. and also include a central limit theorem for weakly negatively associated random variables similar to that of Burton et al.[20].展开更多
文摘The objective of this article is to demonstrate with examples that the two-sided tie correction does not work well. This correction was developed by Cureton so that Kendall’s tau-type and Spearman’s rho-type formulas for rank-biserial correlation yield the same result when ties are present. However, a correction based on the bracket ties achieves the desired goal, which is demonstrated algebraically and checked with three examples. On the one hand, the 10-element random sample given by Cureton, in which the two-sided tie correction performs well, is taken up. On the other hand, two other examples are given, one with a 7-element random sample and the other with a clinical random sample of 31 participants, in which the two-sided tie correction does not work, but the new correction does. It is concluded that the new corrected formulas coincide with Goodman-Kruskal’s gamma as compared to Glass’ formula that matches Somers’ d<sub>Y</sub><sub>|X</sub> or asymmetric measure of association of Y ranking with respect to X dichotomy. The use of this underreported coefficient is suggested, which is very easy to calculate from its equivalence with Kruskal-Wallis’ gamma and Somers’ d<sub>Y</sub><sub>|X</sub>.
文摘Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.
基金Research supported by National Natural Science Foundation of China (No. 19701011)
文摘The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under lower moment conditions or the Lindeberg condition. Results obtained improve a central limit theorem of Roussas[11]for negatively associated fields and the main results of Su and Chi [18]. and also include a central limit theorem for weakly negatively associated random variables similar to that of Burton et al.[20].
