Skip Navigation

Biometrika 1972 59(3):639-648; doi:10.1093/biomet/59.3.639
© 1972 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by FRYER, J. G.
Right arrow Articles by ROBERTSON, C. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

A comparison of some methods for estimating mixed normal distributions

J. G. FRYER* and C. A. ROBERTSON

University of Exeter Riverside
University of California Riverside

*Now at University of North Carolina, Chapel Hill.

Fisher's method of maximum likelihood breaks down when applied to the problem of estimating the five parameters of a mixture of two normal densities from a continuous random sample of size n. Two alternative methods, (i) moment estimates and (ii) multinomial maximum likelihood and niinimum x2 estimates obtained by grouping the underlying variable, are compared both for bias to n{theta}1 and mean squared error to n{theta}2 for a variety of mixed distributions. The methods do not differ essentially with regard to bias but for the mean squared error, the grouped estimates are shown to be more accurate than the moment estimates for most distributions, though the moment estimates seem preferable for distributions which are particularly difficult to estimate. It is also found that the accuracy levels of the grouped maximum likelihood and minimum X2 estimates do not differ greatly.

Key Words: Mixture of normal distributions • Minimum chi-squared estimation • likelihood estimation • Second-order asymptotic theory


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.