Effect of Linear Truncation on a Multinormal Population
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This article is published in Annals of Mathematical Statistics.The article was published on 1950-06-01 and is currently open access. It has received 96 citations till now. The article focuses on the topics: Truncation & Population.read more
Citations
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The Skew-normal Distribution and Related Multivariate Families.
TL;DR: In this paper, the authors provide an introductory overview of a portion of distribution theory which is currently under intense development and illustrate connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non-linear time series, especially in connection with financial data, and more.
Book
The Skew-Normal and Related Families
TL;DR: This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers, and Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques.
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Skewed multivariate models related to hidden truncation and/or selective reporting
Barry C. Arnold,Robert J. Beaver,Adelchi Azzalini,Narayanaswamy Balakrishnan,A. Bhaumik,Dipak K. Dey,Carles M. Cuadras,José María Sarabia +7 more
TL;DR: The univariate skew-normal distribution was introduced by Azzalini in 1985 as a natural extension of the classical normal density to accommodate asymmetry and was extended to include the multivariate analog of the skew normal by Arnold et al. as mentioned in this paper.
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A unified view on skewed distributions arising from selections
TL;DR: In this paper, a new definition of a selection distribution was proposed that encompasses many existing families of multivariate skewed distributions, such as the skew-normal and skew-elliptical distributions, and several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.
References
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Book ChapterDOI
Relations Between Two Sets of Variates
TL;DR: The concept of correlation and regression may be applied not only to ordinary one-dimensional variates but also to variates of two or more dimensions as discussed by the authors, where the correlation of the horizontal components is ordinarily discussed, whereas the complex consisting of horizontal and vertical deviations may be even more interesting.
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Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument
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On the effect of selection performed on some coordinates of a multi-dimensional population.
TL;DR: In this paper a method is presented which makes it possible, under certain assumptions, to correct for the resulting bias and thus reconstruct the means, standard deviations, and correlation coefficients of the original population.