Abstract
IT is common practice to approximate the distribution of the derivative of the log-likelihood, ∂L/∂θ, by a normal distribution with mean zero and variance V = − [E(∂2L/∂θ2)]. Calculations show that the three-moment χ2-approximation: 
can be a considerable improvement over the normal approximation, where a, b and ν (the degrees of freedom of the χ2) are determined so that the right-hand side of (1) has its first three moments in common with (∂L/∂θ), that is: 
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Tiku, M. L., Austral. J. Statist., 7 (in the press).
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TIKU, M. Distribution of the Derivative of the Likelihood Function. Nature 210, 766 (1966). https://doi.org/10.1038/210766a0
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DOI: https://doi.org/10.1038/210766a0
