Associate an optimal normal distribution with a finite numerical discrete data set via extended spline functions

Aim: Given a finite set of cardinal numbers, we approximate the data by an optimal normal distribution based on some criteria. Methods: There are mainly two parts: interpolating the given data via natural spline functions and searching the optimal normal distribution that would minimize the absolute area of the difference function derived from the interpolated density function and the Gaussian distributions. The whole procedures are divided into 10 steps. Results: Our experimental results show the recovered population mean and standard derivation highly depend on the chosen samples. Nonetheless, the interpolated density functions are in the similar shapes of the normal distribution. In addition, the increase of the standard derivation doesn't affect the approximation, though the optimal standard derivation is largely proportional to it. Conclusions: A method with a set of procedures is devised to search the optimal normal distribution for a given set of data. The proposed method takes the absolute area of the difference function into consideration. The interpolated density function is used to match the optimal normal distribution. This matching is much intuitive and straightforward. Other comparative results also show this approach is stable and intuitively justifiable.