Cornish-Fisher expansion  (p.66 of Johnson and Kotz 1994).

[Graphics:../Images/index_gr_1046.gif] in p.66 of JK94 is for the standardized distribution. We assume the cumulants are [Graphics:../Images/index_gr_1047.gif]  The following expression is defined by [Graphics:../Images/index_gr_1048.gif], or [Graphics:../Images/index_gr_1049.gif].

[Graphics:../Images/index_gr_1050.gif]

For w,  the cumulants are [Graphics:../Images/index_gr_1051.gif] We first standardize w and apply cfexpx to the standardized w to get [Graphics:../Images/index_gr_1052.gif].

[Graphics:../Images/index_gr_1053.gif]
[Graphics:../Images/index_gr_1054.gif]
[Graphics:../Images/index_gr_1055.gif]
[Graphics:../Images/index_gr_1056.gif]
[Graphics:../Images/index_gr_1057.gif]
[Graphics:../Images/index_gr_1058.gif]
[Graphics:../Images/index_gr_1059.gif]


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