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On Some Circular Distributions Induced by Inverse Stereographic Projection


On Some Circular Distributions Induced by Inverse Stereographic Projection

Chaubey, Yogendra P. ORCID: https://orcid.org/0000-0002-0234-1429 and Karmaker, Shamal Chandra (2018) On Some Circular Distributions Induced by Inverse Stereographic Projection. Technical Report. Concordia University. Department of Mathematics and Statistics, Montreal, Quebec.

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In earlier studies of circular data, the corresponding probability distributions considered were mostly assumed to be symmetric. However, the assumption of symmetry may not be meaningful for some data. Thus there has been increased interest, more recently, in developing skewed circular distributions. In this article we introduce three skewed circular models based on inverse stereographic projection, originally introduced by Minh and Farnum (2003), by considering three different versions of skewed-t considered in the literature, namely skewed-t by Azzalini (1985), two-piece skewed-t (Fern´andez and Steel, 1998) and skewedt by Jones and Faddy (2003). Shape properties of the resulting circular distributions along with estimation of parameters using maximum likelihood are also discussed in this article. Further, real data sets are used to illustrate the application of the new models. It is found that Azzalini and Jones-Faddy skewed-t versions are good competitors, however, the Jones-Faddy version is computationally more tractable.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Chaubey, Yogendra P. and Karmaker, Shamal Chandra
Series Name:Department of Mathematics & Statistics. Technical Report No. 2/18
Corporate Authors:Concordia University. Department of Mathematics and Statistics
Institution:Concordia University
Date:26 April 2018
  • Natural Sciences and Engineering Research Council
Keywords:Circular data; Skewed-t distribution; Inverse stereographic projection.
ID Code:983833
Deposited By: Yogen Chaubey
Deposited On:07 May 2018 13:26
Last Modified:07 May 2018 13:29


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