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Simulating non‐normal distributions with specified L ‐moments and L ‐correlations
Author(s) -
Headrick Todd C.,
Pant Mohan D.
Publication year - 2012
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2012.00523.x
Subject(s) - kurtosis , mathematics , skew , moment (physics) , normality , skewness , skew normal distribution , class (philosophy) , context (archaeology) , second moment of area , statistics , computer science , physics , geometry , telecommunications , paleontology , classical mechanics , artificial intelligence , biology
This paper derives a procedure for simulating continuous non‐normal distributions with specified L ‐moments and L ‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L ‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L ‐skew and L ‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L ‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L ‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.