Polynomially Adjusted Saddlepoint Density Approximations

摘要

Improved density approximations are obtained by applying certain moment based polynomial adjustments to the saddlepoint approximation. The proposed technique relies on the saddlepoint approximation to the distribution function of a continuous random variable as well. Additionally, a hybrid density estimate is being introduced. Rational functions are also utilized as adjustments. Several numerical examples reveal that, overall, the methodologies that are advocated in this paper consistently produce more accurate distributional approximations.