Estimation of the Mean and Variance of a Univariate Normal Distribution Using Least-Squares via the Differential and Integral Techniques (original) (raw)
Two new approaches (method I and II) for estimating parameters of a univariate normal probability density function are proposed. We evaluate their performance using two simulated normally distributed univariate datasets and their results compared with those obtained from the maximum likelihood (ML) and the method of moments (MM) approaches on the same samples, small n = 24 and large n = 1200 datasets. The proposed methods, I and II have shown to give significantly good results that are comparable to those from the standard methods in a real practical setting. The proposed methods have performed equally well as the ML method on large samples. The major advantage of the proposed methods over the ML method is that they do not require initial approximations for the unknown parameters. We therefore propose that in the practical setting, the proposed methods be used symbiotically with the standard methods to estimate initial approximations at the appropriate step of their algorithms.
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