Analytic saddlepoint approximation for ionization energy loss distributions

The Empirical Saddlepoint Approximation for GMM Estimators

The empirical saddlepoint distribution provides an approximation to the sampling distributions for the GMM parameter estimates and the statistics that test the overidentifying restrictions. The empirical saddlepoint distribution permits asymmetry, non-normal tails, and multiple modes. If identification assumptions are satisfied, the empirical saddlepoint distribution converges to the familiar a...

Saddlepoint approximation method for pricing CDOs

A critical issue in the credit risk industry is the accurate, efficient and robust pricing of collateralized debt obligations (CDO) in a variety of mathematical models. These and many similar basket default products are very complex, due to characteristics of the large number of individual firms upon which they depend. Despite this complexity and because of their versatility, such products have...

Convolution approximation for the energy loss, ionization probability and straggling of fast ions

Normed Likelihood as Saddlepoint Approximation

Barndorff-Nielsen’s formula (normed likelihood with constantinformation metric) has been proffered as an approximate conditional distribution for the maximum-likelihood estimate, based on likelihood functions. Asymptotic justifications are available and the formula coincides with the saddlepoint approximation in full exponential models. It is shown that the formula has wider application than is...

A weak approximation for the Extrema's distributions of Levy processes

‎Suppose that $X_{t}$ is a one-dimensional and real-valued L'evy‎ ‎process started from $X_0=0$‎, ‎which ({bf 1}) its nonnegative‎ ‎jumps measure $nu$ satisfying $int_{Bbb‎ ‎R}min{1,x^2}nu(dx)