A note of the normal power approximation
CM Ramsay - ASTIN Bulletin: The Journal of the IAA, 1991 - cambridge.org
ASTIN Bulletin: The Journal of the IAA, 1991•cambridge.org
The normal power (NP) approximation essentially approximates the random variable X as
the quadratic polynomial X x Y+ y (Y2-\)/6 where X=(X-fi)/a is the standardized variable, Y~
N (0, 1), and/z, ay are the mean, variance skewness of X respectively. The coefficients of this
polynomial are not determined by equating the lower moments. It is shown that matching
these moments does not improve the overall accuracy of the approximation.
the quadratic polynomial X x Y+ y (Y2-\)/6 where X=(X-fi)/a is the standardized variable, Y~
N (0, 1), and/z, ay are the mean, variance skewness of X respectively. The coefficients of this
polynomial are not determined by equating the lower moments. It is shown that matching
these moments does not improve the overall accuracy of the approximation.
Abstract
The normal power (NP) approximation essentially approximates the random variable X as the quadratic polynomial X x Y+ y (Y2-\)/6 where
X=(X-fi)/a is the standardized variable, Y~ N (0, 1), and/z, ay are the mean, variance skewness of X respectively. The coefficients of this polynomial are not determined by equating the lower moments. It is shown that matching these moments does not improve the overall accuracy of the approximation.
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