DocumentCode :
925104
Title :
A nonparametric estimation of the entropy for absolutely continuous distributions (Corresp.)
Author :
Ahmad, Ibrahim A. ; Lin, Pi-erh
Volume :
22
Issue :
3
fYear :
1976
fDate :
5/1/1976 12:00:00 AM
Firstpage :
372
Lastpage :
375
Abstract :
Let 
be an absolutely continuous distribution having a density function 
with respect to the Lebesgue measure. The Shannon entropy is defined as 
. In this correspondence we propose, based on a random sample 
generated from 
, a nonparametric estimate of 
given by 
, where 
is the kernel estimate of 
due to Rosenblatt and Parzen. Regularity conditions are obtained under which the first and second mean consistencies of 
are established. These conditions are mild and easily satisfied. Examples, such as Gamma, Weibull, and normal distributions, are considered.
be an absolutely continuous distribution having a density function with respect to the Lebesgue measure. The Shannon entropy is defined as . In this correspondence we propose, based on a random sample generated from , a nonparametric estimate of given by , where is the kernel estimate of due to Rosenblatt and Parzen. Regularity conditions are obtained under which the first and second mean consistencies of are established. These conditions are mild and easily satisfied. Examples, such as Gamma, Weibull, and normal distributions, are considered.Keywords :
Entropy functions; Nonparametric estimation; Probability functions; Entropy; Equations; Optical arrays; Optical computing; Optical fiber communication; Optical noise; Optical receivers; Statistics; Stochastic processes; Time measurement;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1976.1055550
Filename :
1055550
Link To Document :
