This is a preview. Log in through your library . Abstract This paper presents an asymptotic approximation of marginal tail probabilities for a real-valued function of a random vector, where the ...

Function approximation, a central theme in numerical analysis and applied mathematics, seeks to represent complex functions through simpler or more computationally tractable forms. In this context, ...

Matrix functions, such as the exponential, square root and cosine, play an indispensable role in various fields including quantum mechanics, control theory and numerical solution of differential ...

Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is ...

The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...