Weighted discrepancies and maximum likelihood estimation for discrete distributions |
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Authors: | A.W. Kepm |
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Affiliation: | Department of Statistics , University of St Andrews , Scotland, KY16 9SS |
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Abstract: | The paper shows that many estimation methods, including ML, moments, even-points, empirical c.f. and minimum chi-square, can be regarded as scoring procedures using weighted sums of the discrepancies between observed and expected frequencies The nature of the weights is investigated for many classes of distributions; the study of approximations to the weights clarifies the relationships between estimation methods, and also leads to useful formulae for initial values for ML iteration. |
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Keywords: | weighted discrepancy estimation minimum discrimination information approximate ML methods negative binomial hyper-Poisson Her mite Kemp Poisson-with-zeroes logarithmic distribution. |
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