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Title: A Note on the Normal Power Approximation
Author(s): RAMSAY, Colin M.
Journal: ASTIN Bulletin
Volume: 21    Issue: 1   Date: April 1991   
Pages: 147-150
DOI: 10.2143/AST.21.1.2005407

Abstract :
The normal power (NP) approximation essentially approximates the random variable X as the quadratic polynomial Y+γ(Y2- 1)/6 where , = (X - μ)/σ is the standardized variable, Y ~ N(0, I), and μ, σ γ 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.