Small sample properties of the maximum likelihood estimators of the parameters μ and σ from a grouped sample of a normal population

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Small sample bias and variance of the ML estimators of the parameters μ, and σ of grouped observations from a normal distribution are investigated using Monte Carlo simulation. The usefulness of the estimates of the variance of ML estimators which can be taken from the last iteration of the Scoring and Newton-Raphson algorithm is shown. In addition the small sample levels of some tests on μ and σ which are based on the asymptotic normality of the ML estimators are determined by Monte Carlo simulation