Exponential family and special entropy relation
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CitationBeitollahi, A. (2009). Exponential family and special entropy relation. Maltepe Üniversitesi. s. 111.
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 (θˆ) − HT (θ) ´ in regular exponential models. Let x, βx, Pθ, θ ∈ Θ be a statistical space where Θ is an open subset of Rm. We consider that there exist p.d.f. fθ(x) for the distribution Pθ with respect to a σ-finite measure µ. In 1975 Taneja introduced the generalized entropy as follows, where eitherϕ : [0, ∞) → R is concave and h : R → R is an increasing and concave or ϕ is convex and h is a decreasing and concave. Furthermore we assume that h and ϕ are in C 3 (functions with continuous third derivatives) . If we putϕ(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 fθ(x) be a density of the form  with R(x) = 0, then, Pasha et. al  obtained the formula of divergnce measure by use of Taneja’s entropy in exponential family.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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