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I need to implement the generalized minimum chi-square estimators (alternative to L-moments method and maximum likelihood estimate (MLE)) for estimate the parameters of the gamma distribution. My first question is: for the generalized minimum chi-square estimators method, what is the correct bibliography (paper, book, etc.) to cite? and does anyone know of any package in R (or other software) where this method is implemented?

Thank you all

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    $\begingroup$ Minimum chi-square for estimation is quite old; Neyman and Pearson discuss some of its properties in 1928, but it was being used long before - before estimation by maximum likelihood, for example. You may find Harris and Kanji (1983) "On the Use of Minimum Chi-Square Estimation," Journal of the Royal Statistical Society. Series D (The Statistician) Vol. 32, No. 4 (Dec.), pp. 379-394 of some help in locating additional references. $\endgroup$ – Glen_b Jul 8 '15 at 3:31
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There is a nice paper by Joseph Berkson, "Minimum chi-square, not maximum likelihood!", The Annals of Statistics 1980; 8(3): 457-487. In R there are several packages for least-squares estimation; for minimum chi-square estimation, mipfp may be worth a look.

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  • $\begingroup$ Welcome to the site, @al cliver. At present, this is more of a comment than an answer by our standards. Can you expand on it? Eg, can you give a summary of what is in the paper so future readers can decide if it's something they want to pursue? How would the information in the paper resolve the OP's issue? $\endgroup$ – gung - Reinstate Monica Jul 7 '15 at 14:16
  • $\begingroup$ @Sven It seems to me this is a good answer--it's the question that's marginal, because it's only asking for references and software. Welcome to our site, Al, and thank you for your contribution! $\endgroup$ – whuber Jul 7 '15 at 14:37
  • $\begingroup$ @whuber Agreed. $\endgroup$ – Sven Hohenstein Jul 7 '15 at 14:38
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    $\begingroup$ The Berkson paper is available at project euclid. The paper was submitted in 1977 but not published until 1980; even allowing for the longer time for the discussants to respond, that must have been an arduous review process. $\endgroup$ – Glen_b Jul 8 '15 at 3:08

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