A mixture of normals can have just about any shape (see the book Finite Mixture Models by McLachlan and Peel, which has, near the beginning, a small bestiary of distributions generated with mixtures of normals.); it need not be normal, or even remotely close to normal, if you allow the means and variances to vary.
It could be unimodal, even if the means differ. One way this could happen is if the means are relatively close, compared to the variances. HTH Peter Peter L. Flom, PhD Assistant Director, Statistics and Data Analysis Core Center for Drug Use and HIV Research National Development and Research Institutes 71 W. 23rd St www.peterflom.com New York, NY 10010 (212) 845-4485 (voice) (917) 438-0894 (fax) >>> [EMAIL PROTECTED] 05/03/04 1:29 PM >>> Although apparently "a mixture of two normals, differing in means, can still be unimodal" (orig. Everitt, 1981 "Bimodality and the nature of depression") -- which I don't quite 'see' yet. ----- Original Message ----- From: "rd3d" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, May 03, 2004 10:41 AM Subject: [edstat] Mixture of normal distributions > I would like to know if the mixture of normal distributions is also > considered a normal distribution (with mean and variance of the mixture as > parameters). > If one looks at the graph of the mixture, it is not really bell-shaped, so > I am wondering if it can still be normally distributed. > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
