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New circular model induced by inverse stereographic projection on double exponential model – application to birds migration data. (English) Zbl 1292.60020

Summary: This paper introduces Stereographic Double Exponential Model based on inverse Stereographic Projection or Bilinear (Mobius) Transformation, [D. L. Minh and N. R. Farnum, Commun. Stat., Theory Methods 32, No. 1, 1–9 (2003; Zbl 1025.62003)]. Considering the data set of 13 homing pigeons were released singly in the Toggenburg Valley in Switzerland under sub Alpine conditions (data quoted in [E. Batschelet, Circular statistics in biology. London etc.: Academic Press (1981; Zbl 0524.62104)]), it is shown that the said model is a good fit by most of the tests at various level of significance. The derivation of the characteristic function for Stereographic Double Exponential Model and its trigonometric moments are presented. Relative performance of Stereographic Logistic [Y. Phani, On stereographic circular and semicircular models. Namburu: Acharya Nagarjuna University (Ph.D. thesis)(submitted) (2013], Wrapped Logistic [A. V. Dattatreya Rao et al., Commun. Stat., Theory Methods 36, No. 11, 2027–2035 (2007; Zbl 1122.62046)] and Stereographic Double Exponential models for the live data of 13 birds is studied. Also graphs of pdf of this new Model for various combinations of the parameters are drawn.

MSC:

60E05 Probability distributions: general theory
62H11 Directional data; spatial statistics
62P12 Applications of statistics to environmental and related topics
92D25 Population dynamics (general)

Software:

CircStats; circular
PDFBibTeX XMLCite
Full Text: DOI

References:

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