A Simple Approximation for the Normal Distribution Function via Variational Iteration Method
Keywords:Normal Distribution, Cumulative Distribution Function, Approximations, Variational Iteration Method
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 determined 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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