CornishFisher4
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Function Description
Returns an array of elements
containing the quantiles predicted by the 4th moment CornishFisher asymptotic
expansion for a given input array of probability levels (with elements),
for a given mean, standard deviation, skew and (excess) kurtosis.
The CornishFisher asymptotic expansion is a methodology for
predicting the shape of a (univariate) distributional form merely from the
moments of the distribution. The 4th moment variant uses the mean, standard
deviation, skew and (excess) kurtosis of the distribution.
For standardised returns (zero mean, unit standard
deviation), the 4th moment variant involves estimating the shape of the
quantilequantile plot of the actual versus (standard) Normal distribution
using the following cubic equation, where is
the skew and is
the (excess) kurtosis of the distribution:
In the more generalised case where the mean, , is not
necessarily zero and the standard deviation, is not
necessarily unity the 4th moment variant involves estimating the shape of the
quantilequantile plot as follows:
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