A Simple Approximation for the Normal Distribution Function via Variational Iteration Method


V. K. Shchigolev

In this paper, we obtain some new approximations for the cumulative distribution function of the standard normal
distribution via the He’s Variational Iteration Method. For this end, we consider the cumulative distribution function as
the unknown function to be determine by solving a certain differential equation of the second order that the cumulative
distribution function satisfied subjected with the certain initial conditions. The correction functional in this approach
is constructed here in such a manner that we have one real numerical parameter to be tuned for the best result. Our
approximations to the cumulative distribution function are comparable to other approximations found in the literature
and has the advantage of being a simple expression, that may have potential applications in several areas of applied
sciences. Numerical comparison shows that our approximations are very accurate.


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