Maximum likelihood estimation for constrained parameters of multinomial distributions - Application to Zipf-Mandelbrot models

Izsák, F. (2006) Maximum likelihood estimation for constrained parameters of multinomial distributions - Application to Zipf-Mandelbrot models. Computational Statistics & Data Analysis, 51 (3). pp. 1575-1583. ISSN 0167-9473

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Abstract:	A numerical maximum likelihood (ML) estimation procedure is developed for the constrained parameters of multinomial distributions. The main difﬁculty involved in computing the likelihood function is the precise and fast determination of the multinomial coefﬁcients. For this the coefﬁcients are rewritten into a telescopic product. The presented method is applied to the ML estimation of the Zipf–Mandelbrot (ZM) distribution, which provides a true model in many real-life cases. The examples discussed arise from ecological and medical observations. Based on the estimates, the hypothesis that the data is ZM distributed is tested using a chi-square test. The computer code of the presented procedure is available on request by the author.
Item Type:	Article
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Mathematics of Computational Science (MaCS)
Link to this item:	http://purl.utwente.nl/publications/66721
Official URL:	http://dx.doi.org/10.1016/j.csda.2006.05.008
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