The generalized double Lomax distribution with applications
Keywords:Heavy tailed distribution, Polynomial tails, Leptokurtic, Daily returns
A new probability distribution from the polynomial family has been proposed for modeling heavy-tailed data that are continuous on the whole real line. we have derived some general properties of this distribution and applied it on several data sets of U.S stock market daily returns. The introduced model is symmetric and leptokurtic, it outperforms the peer distributions used for the given data from perspective of information criteria suggesting a new potential candidate for modeling data exhibiting heavy tails.
A. Armagan, D. B. Dunson, J. Lee (2013). Generalized double pareto shrinkage. Statistica Sinica, 23, no. 1, p. 119.
P. Bindu (2011). Estimation of p (x > y) for the double lomax distribution. In Probstat forum. vol. 4, pp. 1-11.
P. Bindu, K. Sangita (2015). Double lomax distribution and its applications. Statistica, 75, no. 3, p. 331.
M. Freimer, G. S. Mudholkar (1992). An analogue of the cherno-borovkov-utev inequality and related characterization. Theory of Probability & Its Applications, 36, no. 3, pp. 589-592.
R. Korwar (1991). On characterizations of distributions by mean absolute deviation and variance bounds. Annals of the Institute of Statistical Mathematics,43, no. 2, pp. 287-295.
K. Lomax (1954). Business failures: Another example of the analysis of failure data. Journal of the American Statistical Association, 49, no. 268, pp. 847-852.
D. Luethi, W. Breymann (2011). ghyp: A package on the generalized hyperbolic distribution and its special cases. R package version, 1, no. 5.
C. Necula, et al. (2009). Modeling heavy-tailed stock index returns using the generalized hyperbolic distribution. Romanian Journal of Economic Forecasting, 10, no. 2, pp. 118-131.
B. Pfaff (2012). Financial risk modelling and portfolio optimization with R.
John Wiley & Sons, United Kingdom.
D. Ruppert (2011). Statistics and data analysis for nancial engineering.
Springer, New York.
C. Shannon (1948). A mathematical theory of communication, bell syst. tech. j., 27: 376-423; 623-656. discrepancy and integration of continuous functions. J. of Approx. Theory, 52, pp. 121-131.
R. D. C. Team, et al. (2011). A language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria.
D. Wuertz, Y. Chalabi, M. Miklovic (2009). fgarch: Rmetrics-autoregressive conditional heteroskedastic modelling. R package version, 2110.
Yahoo (2007). nance. http://nance.yahoo.com. Accessed 22 November 2016.