Re: [R] Off topic -2 Ln Lambda and Chi square

From: Conrad Halling <>
Date: Wed 13 Jul 2005 - 00:45:20 EST

This is a theorem for maximum likelihood tests. See:

Theorem 12.2 (presented without proof), page 391, in "John E. Freund's Mathematical Statistics with Applications", Seventh Edition, by Irwin Miller and Marylees Miller. Upper Saddle River, N.J.: Pearson Prentice Hall, 2004.

    Theorem 12.2: For large n, the distribution of -2 ln Lambda approaches, under very general conditions, the chi-square distribution with 1 degree of freedom.

Theorem 6.3.1 (given with a proof), p. 335, in "Introduction to Mathematical Statistics", Sixth Edition, by RV Hogg, JW McKean, and AT Craig. 2005. Upper Saddle River, New Jersey: Pearson Prentice Hall.

Proofs are also given in:

Testing Statistical Hypotheses, Second Edition, by E. L. Lehmann. New York: John Wiley and Sons, Inc., 1986


Mathematical Statistics, by S. S. Wilkes. New York: John Wiley and Sons, Inc., 1962.

Laura Holt wrote:

>Dear R :
>Sorry for the off topic question, but does anyone know the reference for
>the -2 Ln Lambda following a Chi Square distribution, please?
>Possibly one of Bartlett's?
>Thanks in advance!
>Laura Holt
> mailing list
>PLEASE do read the posting guide!

Conrad Halling

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Received on Wed Jul 13 00:53:17 2005

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