The Gum.el-Barnett fam.ly of bivariate distributions with given m.rginals, is frequently used in theory and applications. This fam.ly has been generalized in several ways. We propose and study a broad generalization b...
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The Gum.el-Barnett fam.ly of bivariate distributions with given m.rginals, is frequently used in theory and applications. This fam.ly has been generalized in several ways. We propose and study a broad generalization by using two differentiable functions. We obtain som. properties and describe particular cases.
We present in three parts different concepts of correlation and statistical association, with som. historical notes, starting with Galton's notion of correlation, subsequently im.roved by Pearson. Continuing in th...
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We present in three parts different concepts of correlation and statistical association, with som. historical notes, starting with Galton's notion of correlation, subsequently im.roved by Pearson. Continuing in this first part, we discuss the correlation ratio, the intraclass correlation, m.ltiple correlation, and redundancy analysis. Throughout we use the classic data set of Galton on the heights of parents and their children. In the second part we explain how these sam. data can be studied from.a m.ltivariate viewpoint, using canonical correlation analysis, Procrustes correlation and sim.le/m.ltiple correspondence analysis. For correspondence analysis, we use the sam. data as categorized by Galton into intervals of heights for the parents and their children. In this part we also m.ke an incursion into the continuous form.of correspondence analysis. The third part is dedicated to bivariate distributions, where we give the m.in results of bivariate distributions with given m.rginals, com.enting on the correlations of Spearm.n and Kendall. Seeing that a bivariate distribution can be generated using a copula, we fit Galton's data to two copulas: the Gaussian copula and the copula which has the best fit. (C) 2021 Published by Elsevier Inc.
The Farlie-Gum.el-m.rgensten (FGm. fam.ly of bivariate distributions with given m.rginals, is frequently used in theory and applications and has been generalized in m.ny ways. With the help of two auxiliary distributi...
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The Farlie-Gum.el-m.rgensten (FGm. fam.ly of bivariate distributions with given m.rginals, is frequently used in theory and applications and has been generalized in m.ny ways. With the help of two auxiliary distributions, we propose another generalization and study its properties. After defining the rank of a distribution as the cardinal of the set of canonical correlations, we prove that som. well-known distributions have practically rank two. Consequently we introduce several extended FGm.fam.lies of rank two and study how to approxim.te any bivariate distribution to a sim.ler one belonging to this fam.ly.
Hoeffding's lem.a provides a representation of the covariance of two random.variables in term. of the difference between the joint and m.rginal distributions. This article proposes a m.ltivariate generalization of...
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Hoeffding's lem.a provides a representation of the covariance of two random.variables in term. of the difference between the joint and m.rginal distributions. This article proposes a m.ltivariate generalization of the covariance between functions of bounded variation in the sem.algebra of rectangles on R-2k. Som. applications include the covariance inequality am.ng functions where the variables are positive orthant dependent.
We present a unified approach to describing and linking several m.thods for representing categorical data in a contingency table. These m.thods include: correspondence analysis, Hellinger distance analysis, the log-ra...
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We present a unified approach to describing and linking several m.thods for representing categorical data in a contingency table. These m.thods include: correspondence analysis, Hellinger distance analysis, the log-ratio alternative, which is appropriate for com.ositional data, and the non-sym.etrical correspondence analysis. We also present two solutions working with cum.ulative frequencies.
A continuous random.variable is expanded as a sum.of a sequence of uncorrelated random.variables. These variables are principal dim.nsions in continuous scaling on a distance function, as an extension of classic scali...
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A continuous random.variable is expanded as a sum.of a sequence of uncorrelated random.variables. These variables are principal dim.nsions in continuous scaling on a distance function, as an extension of classic scaling on a distance m.trix. For a particular distance, these dim.nsions are principal com.onents. Then som. properties are studied and an inequality is obtained. Diagonal expansions are considered from.the sam. continuous scaling point of view, by m.ans of the chi-square distance. The geom.tric dim.nsion of a bivariate distribution is defined and illustrated with copulas. It is shown that the dim.nsion can have the power of continuum.
We find som. properties and eigendecom.ositions of two integral operators related to copulas. By using an inner product between two functions via an extension of the covariance, we study the countable set of eigenpair...
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We find som. properties and eigendecom.ositions of two integral operators related to copulas. By using an inner product between two functions via an extension of the covariance, we study the countable set of eigenpairs, which is related to the set of canonical correlations and functions. Then a canonical analysis on the so-called cuadras Auge fam.ly of copulas is perform.d, showing the continuous dim.nsionality of this distribution. A diagonal expansion in term. of an integral is obtained. As a consequence, this continuous expansion allows us to generate a wide fam.ly of copulas. (C) 2015 Elsevier Inc. All rights reserved.
Objective: To determ.ne the influence of radical prostatectom. (RP) and external beam.radiation therapy (EBRT) on the hypothalam.c pituitary axis of 120 m.n with clinically localized prostate cancer treated with RP or...
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Objective: To determ.ne the influence of radical prostatectom. (RP) and external beam.radiation therapy (EBRT) on the hypothalam.c pituitary axis of 120 m.n with clinically localized prostate cancer treated with RP or EBRT exclusively. m.terials and m.thods: 120 patients with localized prostate cancer were enrolled. Ninety two patients underwent RP and 28 patients EBRT exclusively. We m.asured serum.levels of luteinizing horm.ne, follicle stim.lating horm.ne (FSH), total testosterone (T), free testosterone, and estradiol at baseline and at 3 and 12 m.nths after treatm.nt com.letion. Results: Patients undergoing RP were younger and presented a higher prostate volum. (64.3 vs. 71.1 years, p < 0.0001 and 55.1 vs. 36.5 g, p < 0.0001;respectively). No differences regarding serum.horm.nal levels were found at baseline. Luteinizing horm.ne and FSH levels were significantly higher in those patients treated with EBRT at three m.nths (luteinizing horm.ne 8,54 vs. 4,76 U/l, FSH 22,96 vs. 8,18 U/l, p < 0,0001) while T and free testosterone levels were significantly lower (T 360,3 vs. 414,83 ng/dl, p 0,039;free testosterone 5,94 vs. 7,5 pg/m., p 0,018). At 12 m.nths FSH levels rem.ined significantly higher in patients treated with EBRT com.ared to patients treated with RP (21,01 vs. 8,51 U/l, p <0,001) while T levels rem.ined significantly lower (339,89 vs. 402,39 ng/dl, p 0,03). Conclusions: Prostate cancer treatm.nt influences the hypothalam.c pituitary axis. This influence seem. to be m.re im.ortant when patients with prostate cancer are treated with EBRT rather than RP. m.re studies are needed to elucidate the role that prostate m.y play as an endocrine organ. (C) 2016 AEU. Published by Elsevier Espana, S.L.U. All rights reserved.
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