Abstract
In this paper, Romanowski’s modified normal distribution is considered from the mathematical standpoint. Initially, the characteristic function is computed. This function is then utilized to (1) compute moments, (2) demonstrate normal tendency as the modulating (“a”) parameter tends to infinity, (3) to formulate the modified normal distribution in terms of well known classical functions. To complete this mathematical consideration, the probability distribution is formulated in terms of tabulated functions. The paper is concluded with a discussion on the direction for further research.
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McLane, P.J. Mathematical considerations of the modified normal distribution. Bull. Geodesique 83, 9–20 (1967). https://doi.org/10.1007/BF02526102
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DOI: https://doi.org/10.1007/BF02526102