WRAPPED FLEXIBLE SKEW LAPLACE DISTRIBUTION

Year 2018, Volume: 11 Issue: 3, 53 - 64, 31.12.2018

Abdullah Yılmaz

Abstract

We introduce a new circular distribution named as wrapped flexible skew Laplace distribution. This distribution is the generalization of wrapped Laplace which was introduced by Jammalamadaka and Kozubowski 2003 and has more flexibility properties in terms of skewness, kurtosis, unimodality or bimodality. We also derive expressions for characteristic function, trigonometric moments, coefficients of skewness and kurtosis. We analyzed two popular datasets from the literature to show the good modeling ability of the WFSL distribution.

Keywords

Circular distribution, flexible skew laplace distribution, wrapped distribution, laplace distribution, skew-symmetric distribution

References

• Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12 (2), 171–178.
• Dattatreya Rao, A., I. Ramabhadra Sarma, and S. Girija (2007). On wrapped version of some life testing models. Communications in Statistics-Theory and Methods, 36 (11), 2027–2035.
• Fernandez-Duran, J. (2004). Circular distributions based on nonnegative trigonometric sums. Biometrics, 60 (2), 499–503.
• Fisher, N. I. (1995). Statistical Analysis of Circular Data. Cambridge University Press.
• Jammalamadaka, S. R. and T. Kozubowski (2003). A new family of circular models: The wrapped laplace distributions. Advances and applications in statistics, 3 (1), 77–103.
• Jammalamadaka, S. R. and T. J. Kozubowski (2004). New families of wrapped distributions for modeling skew circular data. Communications in Statistics-Theory and Methods, 33 (9), 2059–2074.
• Jammalamadaka, S. R. and A. Sengupta (2001). Topics in circular statistics, Volume 5. World Scientific.
• Joshi, S. and K. K. Jose (2018). Wrapped lindley distribution. Communications in Statistics-Theory and Methods, 47 (5), 1013–1021.
• Mardia, K. (1972). Statistics of Directional Data. London: Academic Press.
• Mardia, K. V. and P. E. Jupp (2009). Directional Statistics, Volume 494. John Wiley-Sons.
• Pewsey, A. (2000). The wrapped skew-normal distribution on the circle. Communications in Statistics- Theory and Methods, 29 (11), 2459–2472.
• Phani, Y., S. Girija, and A. Dattatreya Rao (2012). Circular model induced by inverse stereographic projection on extreme-value distribution. Engineering Science and Technology, 2 (5), 881–888.
• Umbach, D. and S. R. Jammalamadaka (2009). Building asymmetry into circular distributions. Statistics & Probability Letters, 79 (5), 659–663.
• Yilmaz, A. (2016). The flexible skew laplace distribution. Communications in Statistics-Theory and Methods, 45 (23), 7053–7059.
• Yilmaz, A. and C. Bi¸cer (2018). A new wrapped exponential distribution. Mathematical Sciences, 12 (4), 285–293.