Surface curvature analysis of bivariate normal distribution: A Covid-19 data application on Turkey
Makaleler > Tam Makale · 2022
Yazarlar: Vahide Bulut, Mustafa Serdar KORUKOĞLU
Regional Statistics, Uluslararası, Scopus, 2022, cilt 12, ss 3-26
DOI: 10.15196/rs120401
Özet
Introduction and literature reviewPrincipal curvatures, principal directions, and normals are used in 3D computer vision to solve basic tasks, such as segmentation, surface classification, surface reconstruction, and registration Krsek et al. (1998).Since the principal curvatures at a surface point are invariant properties, these curvatures are used for surface characterisation.Researchers have studied many methods to estimate the Gaussian and mean curvatures on various surfaces such as faces and human bodies.In Tanaka et al. (1998), the authors presented a correlation-based face recognition approach based on the analysis of principal curvatures.The authors Vemuri et al. (1986) used principal curvatures for shape recognition from range data, while in Deng et al. (2007), the authors used these curvatures for object recognition.In Bedi et al. (1997), two methods for machining complex three-dimensional surfaces on 4 and 5 axis machines are proposed to align the principal axis of the curvature of the machining surface with that of the machined surface to increase the volume of the removed material.Authors Floro-Chason (2001) studied the use of a curvature technique called a multi-beam optical stress sensor.In Sboui et al. (2017), the authors proposed a local surface description around the 3D human body extremities based on the mean of the principal curvature field values on the intrinsic Darcyan parameterisation.Justin et al. (Lev et al. (2017)) presented a new local measure based on the principal curvatures of a point cloud for 3D shape recognition.In Tremblay-Darveau et al. (2018), the authors showed that the principal curvature detection could significantly improve the 3D rendering of relatively noisy ultrasound angiograms without degrading the spatial resolution.Moreover, the authors Wang et al. (2018) proposed a shape-similarity measurement approach based on principal curvatures.The normal distribution of statistics has great importance in different fields such as economics, medicine, actuarial sciences, and engineering.Azzalini (1985) studied the standard normal-density function and its properties.In Azzalini-Chiogna (2004), the authors gave some exact probability results on the stress-strength model in the case of skew-normal variates.Henze (1986) presented a probabilistic representation of the skew-normal distribution in the normal and truncated normal law.In Branco-Dey (2001), the authors proposed a new class of multivariate skew-elliptical distributions, which bring additional flexibility of modeling skewed data.A class of multivariate unified skew-elliptical distributions is presented in Arellano-Valle-Genton (2010).The authors proposed a new model distribution, known as the bivariate Weibull-Geometric distribution in Kundu-Gupta (2014).In Roozegar-Jafari (2017), the authors expressed the bivariate generalized linear failure rate-power series model as a new class of bivariate distributions.The authors studied a new bivariate distribution and its distributional properties with normal geometric distribution marginal in Mahmoudi-Mahmoodian (2017). In Omair et al. (2018), the authors introduced a new bivariate model and its distributional properties combining negative binomial and geometric distributions.In Jafari et al. (2018), the authors