Abstract
In practical life usually we come across angular or periodic data which needs distributions that are invariant of zero direction and sense of rotation for analysis. Inverse stereographic projection/ Bilinear transformation defined by a one to one mapping generate a class of probability distributions on unit circle that are flexible to analyse circular data. The probability density f unction of many life testing models ranges from 0 to ∞ . Aiming to construct new circular model by applying Inverse Stereographic Projection, we consider Double Weibull distribution and derive density, distribution and characteristic functions of new circular model coined by us Stereographic Double Weibull distribution. Also an attempt is made to study the mathematical aspects in evaluating trigonometric moments of new circular model and present the population characteristics. Goodness of fit to a live data is verified.
Highlights
Wrapped versions of some life testing models on a unit circle were derived by Dattatreya Rao et al (2007) and Girija (2010)
Inverse stereographic projection/ Bilinear transformation defined by a one to one mapping generate a class of probability distributions on unit circle that are flexible to analyse circular data
It is proposed that one way of constructing circular models by inducing inverse stereographic projection on linear models
Summary
Wrapped versions of some life testing models on a unit circle were derived by Dattatreya Rao et al (2007) and Girija (2010). It is proposed that one way of constructing circular models by inducing inverse stereographic projection on linear models. Dattatreya Rao et al (2011) applied bilinear transformation on Cardioid distribution to generate Cauchy-Type models and presented a differential approach to circular models. Balakrishna and Kocherla Kota (1985) introduced double Weibull distribution by reflecting Weibull Symmetrically to and studied linear estimation of location and scale parameters. He gave coefficients to find linear estimates of location and scale parameters for specified values of the shape parameter. Based on the approach of Minh et al (2003) and Toshihiro Abe et al (2010) circular models are derived by inducing inverse stereographic projection on double Weibull model. Data set of 13 homing pigeons is modelled through the circular models by applying goodness of fit tests
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