Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A New Family of Semicircular Models: The Semicircular Laplace Distributions

  • Published : 2008.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

It is developed that a family of the semicircular Laplace distributions for modeling semicircular data by simple projection method. Mathematically it is simple to simulate observations from a semicircular Laplace distribution. We extend it to the l-axial Laplace distribution by a simple transformation for modeling any arc of arbitrary length. Similarly we develop the l-axial log-Laplace distribution based on the log-Laplace distribution. A bivariate version of l-axial Laplace distribution is also developed.

Keywords

References

  1. Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York
  2. Fisher, N. I. (1993). Statistical Analysis of Circular Data, Cambridge University Press, Cambridge
  3. Gradshteyn, I. S. and Ryzhik, I. M. (2007). Table of Integrals, Series, and Products, (7th ed.), Academic Press, San Diego
  4. Guardiola, J. H. (2004). The Semicircular Normal Distribution, Ph. D. Dissertation, Baylor University, Institute of Statistics
  5. Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in Circular Statistics, World Scientific Publishing, Singapore
  6. Johnson, N. L. and Kotz, S. (1972). Continuous Multivariate Distributions, John Wiley & Sons, New York
  7. Jones, T. A. (1968). Statistical analysis of orientation data, Journal of Sedimentary Petrology, 38, 61-67
  8. Kim, H. M. (2008). New family of the t distributions for modeling semicircular data, Communications of the Korean Statistical Society, To appear
  9. Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics, John Wiley & Sons, Chichester
  10. Ugai, S., Kato, K., Nishijima, M. and Kan, T. (1977), Characteristics of raindrop size and raindrop shape, Open Symposium URSI Commission F, 225-230

Cited by

  1. A Projected Exponential Family for Modeling Semicircular Data vol.23, pp.6, 2010, https://doi.org/10.5351/KJAS.2010.23.6.1125