Simulation of the p-generalized Gaussian distribution

References

• Subbotin , M. T. 1923 . On the law of frequency errors . Mat. Sb. , 31 : 296 – 301 .
   Google Scholar
• Box , G. E.P. and Tiao , C. G. 1973 . Bayesian Inference in Statistical Analysis , New York : Wiley .
   Google Scholar
• Johnson , N. L. , Kotz , S. and Balakrishnan , N. 1994 . Continuous Univariate Distributions , 2 , Vol. 1 , New York : Wiley .
   Google Scholar
• Moszyńska , M. and Richter , W.-D. 2011 . Reverse triangle inequality. Anti-norms and semi-anti-norms . Studia Sci. Math. Hungarica , accepted for publication
   Web of Science ®Google Scholar
• Pogány , T. K. and Nadarajah , S. 2010 . On the characteristic function of the generalized normal distribution . C. R. Math. , 348 ( 3 ) : 203 – 206 .
   Google Scholar
• Nardon , M. and Pianca , P. 2009 . Simulation techniques for generalized Gaussian densities . J. Statist. Softw. Simul , 79 ( 11 ) : 1317 – 1329 . (doi:10.1080/00949650802290912)
   Web of Science ®Google Scholar
• Saatci , E. and Akan , A. 2010 . Respiratory parameter estimation in non-invasive ventilation based on generalized Gaussian noise models . Signal process. , 90 ( 2 ) : 480 – 489 . (doi:10.1016/j.sigpro.2009.07.015)
   Web of Science ®Google Scholar
• Box , G. E.P. and Muller , M. E. 1958 . A note on the generation of random normal deviates . Ann. Math. Statist. , 29 ( 2 ) : 610 – 611 . (doi:10.1214/aoms/1177706645)
   Google Scholar
• Marsaglia , G. and Bray , T. 1964 . A convenient method for generating normal variables . SIAM Rev. , 6 : 260 – 264 . (doi:10.1137/1006063)
   Web of Science ®Google Scholar
• Neumann , J. v. 1951 . “ Various techniques used in connection with random digits ” . In Monte Carlo Methods , Edited by: Householder , A. S. , Forsythe , G. E. and Germond , H. H. 36 – 38 . Washington , DC : National Bureau of Standards . Applied Mathematics Series 12
   Google Scholar
• Richter , W.-D. 2007 . Generalized spherical and simplicial coordinates . J. Math. Anal. Appl. , 336 : 1187 – 1202 . (doi:10.1016/j.jmaa.2007.03.047)
   Web of Science ®Google Scholar
• Richter , W.-D. 2009 . Continuous ln, p-symmetric distributions . Lithuanian Math. J. , 49 : 93 – 108 . (doi:10.1007/s10986-009-9030-3)
   Web of Science ®Google Scholar
• Rubinstein , R. Y. 1981 . Simulation and the Monte Carlo Method , 1 , New York : Wiley .
   Google Scholar
• Jöhnk , M. D. 1964 . Erzeugung von betaverteilten und gammaverteilten Zufallszahlen . Metrika , 8 : 5 – 15 . (doi:10.1007/BF02613706)
   Web of Science ®Google Scholar
• Devroye , L. 1986 . Non-Uniform Random Variate Generation , Berlin : Springer .
   Google Scholar
• Malham , S. J.A. and Wiese , A. 2011 . Positive volatility simulation in the Heston model, submitted . Available at arXiv:0802.4411v3
   Google Scholar
• Hörmann , W. , Leydold , J. and Derflinger , G. 2004 . Automatic Nonuniform Random Variate Generation , Berlin : Springer .
   Google Scholar
• Marsaglia , G. and Tsang , W. W. 2000 . The Ziggurat method for generating random variables . J. Statist. Softw. , 5 : 1 – 7 .
   Google Scholar
• Marsaglia , G. 1998 . The Monty Python method for generating random variables . ACM Trans. Math. Softw. , 24 ( 3 ) : 341 – 350 . (doi:10.1145/292395.292453)
   Web of Science ®Google Scholar
• Marsaglia , G. and Tsang , W. W. 1984 . A fast, easily implemented method for sampling from decreasing or symmetric unimodal density functions . SIAM J. Sci. Statist. Comput. , 5 : 349 – 359 . (doi:10.1137/0905026)
   Web of Science ®Google Scholar
• Brent , R. 1973 . Algorithms for Minimization Without Derivatives , Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• Sachs , L. and Hedderich , J. 2009 . Angewandte Statistik , Berlin : Springer . 13. Auflage
   Google Scholar
• Becker , R. A. , Chambers , J. M. and Wilks , A. R. 1988 . The New S Language , Pacific Grove , CA : Brooks/Cole & Wodsworth Computer Science Series .
   Google Scholar
• Ahrens , J. H. 1993 . Sampling from general distributions by suboptimal division of domains . Grazer Math. Ber. , 319 : 1 – 20 .
   Google Scholar
• Ahrens , J. H. 1995 . A one-table method for sampling from continuous and discrete distributions . Computing , 54 ( 2 ) : 127 – 146 . (doi:10.1007/BF02238128)
   Web of Science ®Google Scholar