Exponential family and special entropy relation
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
In this article ,we derive Taneja’s entropy formula for exponential family so that the derived formula by Menendez (2000) is a special case of it. We will obtain proper Taneja’s entropy formulas for Gamma, Beta and Normal distributions. At last we will review the asymptotic distribution of ³ HT (?ˆ) ? HT (?) ´ in regular exponential models. Let x, ?x, P?, ? ? ? be a statistical space where ? is an open subset of Rm. We consider that there exist p.d.f. f?(x) for the distribution P? with respect to a ?-finite measure µ. In 1975 Taneja introduced the generalized entropy as follows, where either? : [0, ?) ? R is concave and h : R ? R is an increasing and concave or ? is convex and h is a decreasing and concave. Furthermore we assume that h and ? are in C 3 (functions with continuous third derivatives) . If we put?(x) = x r log x andh(x) = ?2 r?1x then the Taneja’s entropy formula is obtained. The exponential family of kparameter distribution is, Theorem: Let f?(x) be a density of the form [1] with R(x) = 0, then, Pasha et. al [1] obtained the formula of divergnce measure by use of Taneja’s entropy in exponential family.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Beitollahi, A. (2009). Exponential family and special entropy relation. Maltepe Üniversitesi. s. 111.
