DocumentCode :
3127188
Title :
Information divergence is more χ2-distributed than the χ2-statistics
Author :
Harremoës, Peter ; Tusnády, Gábor
Author_Institution :
Copenhagen Bus. Coll., Copenhagen, Denmark
fYear :
2012
fDate :
1-6 July 2012
Firstpage :
533
Lastpage :
537
Abstract :
For testing goodness of fit it is very popular to use either the χ2-statistic or G2-statistics (information divergence). Asymptotically both are χ2-distributed so an obvious question is which of the two statistics that has a distribution that is closest to the χ2-distribution. Surprisingly, when there is only one degree of freedom it seems like the distribution of information divergence is much better approximated by a χ2-distribution than the χ2-statistic. For random variables we introduce a new transformation that transform several important distributions into new random variables that are almost Gaussian. For the binomial distributions and the Poisson distributions we formulate a general conjecture about how close their transform are to the Gaussian. The conjecture is proved for Poisson distributions.
Keywords :
Gaussian distribution; Poisson distribution; binomial distribution; random processes; statistical testing; χ2-statistic; G2-statistics; Gaussian; Poisson distribution; binomial distribution; information divergence; random variable; testing goodness; Approximation methods; Information theory; Random variables; Standards; Testing; Transforms;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
ISSN :
2157-8095
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
Type :
conf
DOI :
10.1109/ISIT.2012.6284247
Filename :
6284247
Link To Document :
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