On Bimodal Offset Cauchy Distribution

The bivariate Cauchy distribution has received applications in many areas, including biological analyses, clinical trials, stochastic modeling of decreasing failure rate life components, study of labour turnover, queuing theory and reliability (Nayak (1987) and Lee and Gross (1991)). In the study of biological analyses, clinical trials and reliability circular distributions will yield suitable results. Circular data arises in a number of different areas such as geological, meteorological, biological and industrial sciences. It is not suggestive to use standard statistical techniques to model circular data, due to the circular geometry of the sample space (p.2 Jammalamadaka and Sen Gupta (2001). It is possible to construct a circular model by transforming a bivariate linear random variate to just its directional component and the resultant model is called ‘offset distribution’. In the literature most of the available circular models were constructed by wrapping a linear model. In recent years some wrapped models were constructed by Dattatreya Rao et al (2007). Here an attempt is made to exploit method of offsetting on Bivariate Cauchy distribution to construct a circular model named by us “OFFSET CAUCHY DISTRIBUTION (OC)”. The characteristic function of the Offset Cauchy model is derived and its characteristics are discussed.