Abstract
One of the available techniques of constructing circular models, offsetting has not been paid much attention, in particular for the construction of arc models. Here making use of the method of offsetting on bivariate distributions, l-arc models are constructed. The method of transforming a bivariate linear random variable to its directional component is called OFFSETTING and the respective distribution of directional component is called OFFSET DISTRIBUTION which is a univariate circular model. By employing the concept of arc models, we obtain Offset Semicircular Cauchy model. Here we obtain Arc models directly by applying offsetting on a linear bivariate models such as Bivariate Beta and Bivariate Exponential models. Existence of these arc models occur in natural phenomenon. Some of the newly proposed semicircular/arc models are bimodal models and the population characteristics of the offset semicircular and arc models are studied.
Highlights
A good number of circular models by wrapping some life testing models on the unit circle were derived by Dattatreya Rao [6]and Girija [9]Quite a lot of work was done on circular models defined on the unit circle Fisher [8]; Jammalamadaka and Sengupta [11]; Mardia and Jupp [12]
Any distribution defined for angular data can be constructed by applying offsetting on a linear bivariate distribution
The method of offsetting on bivariate distribution is used as the motivation for construction of new arc models, in particular, bimodal distributions
Summary
A good number of circular models by wrapping some life testing models on the unit circle were derived by Dattatreya Rao [6]and Girija [9]Quite a lot of work was done on circular models defined on the unit circle Fisher [8]; Jammalamadaka and Sengupta [11]; Mardia and Jupp [12]. The method of offsetting on bivariate distribution is used as the motivation for construction of new arc models, in particular, bimodal distributions. We obtain Arc models directly by applying offsetting on a linear bivariate models such as Bivariate Beta and Bivariate Exponential models in which both the variables are defined in [0, 1]and in particular, sum of the variables of Bivariate Beta distribution lies in [0, 1], irrespective of imposing restriction on circular random variable. Existence of these arc models occur in natural phenomenon. Expressions in Mardia and Jupp [12] are employed to study the properties of the offset circular, semicircular and arc models
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