Approximating Distributions by Extended Generalized Lambda Distribution (XGLD)

References

• Asquith , W. H. ( 2007 ). L-moments and TL-moments of the generalized lambda distribution . Computational Statistics & Data Analysis 51 : 4484 – 4496 .
   Web of Science ®Google Scholar
• Bigerelle , M. , Najjar , D. , Fournier , B. , Rupin , N. , Iost , A. ( 2005 ). Application of lambda distributions and bootstrap analysis to the prediction of fatigue lifetime and confidence intervals . International Journal of Fatigue 28 : 223 – 236 .
   Web of Science ®Google Scholar
• Bratley , P. , Fox , B. ( 1988 ). Algorithm 659: implementing Sobol's quasirandom sequence generator . ACM Transactions on Mathematical Software 14 ( 1 ): 88 – 100 .
   Web of Science ®Google Scholar
• D'Agostino , R. , Stephens , M. ( 1986 ). Goodness-of-Fit Techniques, Statistics: Textbooks and Monographs . New York : Marcel Dekker .
   Google Scholar
• Delaney , H. D. , Vargha , A. ( 2000 ). The effect on non-normality on student's two-sample t-test. Annual Meeting of the American Educational Research Association , New Orleans , LA , April 24–28 , pp. 1 – 30 .
   Google Scholar
• Dengiz , B. ( 1988 ). The generalized lambda distribution in simulation of M/M/1 queue systems . Journal of the Faculty of Engineering and Architecture of Gazi University 3 : 161 – 171 .
   Google Scholar
• Devroye , L. ( 2006 ). Non-Uniform Random Variate Generation . New York : Springer .
   Google Scholar
• Filliben , J. J. ( 1969 ). Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution. Ph.D. Dissertation, Princeton University , Princeton , NJ .
   Google Scholar
• Filliben , J. J. ( 1975 ). The probability plot correlation coefficient test for normality . Technometrics 17 ( 111 ): 111 – 117 .
   Google Scholar
• Fournier , B. , Rupin , N. , Bigereller , M. , Najjar , D. , Iost , A. , Wilcox , R. ( 2007 ). Estimating the parameters of a generalized lambda distribution . Computational Statistics & Data Analysis 51 : 2813 – 2835 .
   Web of Science ®Google Scholar
• Fournier , B. , Rupin , N. , Bigerelle , M. , Najjar , D. , Iost , A. ( 2006 ). Application of the generalized lambda distributions in a statistical process control methodology . Journal of Process Control 16 : 1087 – 1098 .
   Web of Science ®Google Scholar
• Freimer , M. , Mudholkar , G. , Kollia , G. , Lin , C. ( 1988 ). A study of the generalized Tukey lambda family . Communications in Statistics, Theory and Methods 17 ( 10 ): 3547 – 3567 .
   Web of Science ®Google Scholar
• Ganeshan , R. ( 2001 ). Are more suppliers better?: generalizing the Gau and Ganeshan procedure . Journal of the Operational Research Society 52 : 122 – 123 .
   Web of Science ®Google Scholar
• Headrick , T. C. , Mugdadi , A. ( 2006 ). On simulating multivariate non-normal distributions from the generalized lambda distribution . Computational Statistics & Data Analysis 50 : 3343 – 3353 .
   Web of Science ®Google Scholar
• Karian , Z. A. , Dudewicz , E. J. ( 2000 ). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Method . Boca Raton , FL : CRC Press .
   Google Scholar
• Karian , Z. A. , Dudewicz , E. J. ( 2003 ). Comparison of GLD fitting methods: superiority of percentile fits to moments in L2 norm . Jouranal of the Iranian Statistical Society 2 : 171 – 187 .
   Google Scholar
• Karian , Z. A. , Dudewicz , E. J. , McDonald , P. ( 1996 ). The extended generalized lambda distribution system for fitting distributions to data: history, completion of theory, tables applications, the “Finalword” on moments fits . Communications in Statistics—Simulation and Computing 25 : 611 – 642 .
   Web of Science ®Google Scholar
• Karvanen , J. ( 2003 ). Generation of Correlated Non-Gaussian Random Variables from Independent Components. Fourth International Symposium on Independent Component Analysis and Blind Signal Separation , Nara , Japan , pp. 203 – 207 .
   Google Scholar
• Karvanen , J. , Nuutinen , A. ( 2008 ). Characterizing the generalized lambda distribution by L-moments . Computational Statistics & Data Analysis 52 : 1971 – 1983 .
   Web of Science ®Google Scholar
• King , R. , MacGillivray , H. (1999). A starship estimation method for the generalized lambda distributions. Australian & New Zealand Journal of Statistics 41:353–374.
   Web of Science ®Google Scholar
• Lakhany , A. , Mausser , H. ( 2000 ). Estimating the parameters of the generalized lambda distribution . Algo Research Quarterly 3 ( 3 ): 47 – 58 .
   Google Scholar
• Najjar , D. , Bigerelle , M. , Lefebvre , C. , Iost , A. ( 2003 ). A new approach to predict the pit depth extreme value of a localized corrosion process . ISIJ 43 : 720 – 725 .
   Google Scholar
• Nelder , J. , Mead , R. ( 1965 ). A simplex method for function minimization . Computer Journal 7 : 308 – 313 .
   Web of Science ®Google Scholar
• Öztürk , A. , Dale , R. F. ( 1982 ). A study of fitting the generalized lambda distribution to solar radiation data . Journal of Applied Meteorology 21 : 995 – 1004 .
   Google Scholar
• Öztürk , A. , Dale , R. F. ( 1985 ). Least squares estimation of the parameters of the generalized lambda distribution . Technometrics 27 ( 1 ): 81 – 84 .
   Web of Science ®Google Scholar
• Ramberg , J. , Schmeiser , B. ( 1974 ). An approximate method for generating asymmetric random variables . Communications of the ACM 17 ( 2 ): 78 – 82 .
   Web of Science ®Google Scholar
• Ramberg , J. S. , Schmeiser , B. W. ( 1972 ). An approximate method for generating symmetric random variables . Communications of the ACM 15 : 987 – 990 .
   Web of Science ®Google Scholar
• Ramberg , J. S. , Dudewicz , E. , Tadikamalla , P. , Mykytka , E. ( 1979 ). A probability distribution and its use in fitting data . Technometrics 21 : 201 – 214 .
   Web of Science ®Google Scholar
• Su , S. ( 2007 ). Numerical maximum log likelihood estimation for generalized lambda distributions . Computational Statistics & Data Analysis 51 : 3983 – 3998 .
   Web of Science ®Google Scholar
• Tukey , J. W. ( 1962 ). The future of data analysis . Annals of Mathematical Statistics 33 ( 1 ): 1 – 67 .
   Google Scholar
• Upadhyay , R. R. , Ezekoye , O. A. ( 2008 ). Treatment of design fire uncertainty using quadrature method of moments . Fire Safety Journal 43 : 127 – 139 .
   Web of Science ®Google Scholar