Complete monotonicity of some entropies
Sign Up to like & getrecommendations! Published in 2017 at "Periodica Mathematica Hungarica"
DOI: 10.1007/s10998-016-0177-5
Abstract: It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and… read more here.
Keywords: monotonicity; complete monotonicity; monotonicity entropies;
Complete monotonicity of a function related to the binomial probability
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.10.077
Abstract: Abstract Let k and n be integers with 0 ≤ k ≤ n and p ∈ ( 0 , 1 ) . We prove that the function G ( a ) = G k ,… read more here.
Keywords: complete monotonicity; monotonicity function; binomial probability; function ... See more keywords
Complete monotonicity involving some ratios of gamma functions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-017-1527-4
Abstract: In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As… read more here.
Keywords: complete monotonicity; involving ratios; gamma functions; monotonicity involving ... See more keywords
Complete monotonicity involving the divided difference of polygamma functions
Sign Up to like & getrecommendations! Published in 2023 at "Applicable Analysis and Discrete Mathematics"
DOI: 10.2298/aadm210630007y
Abstract: For r, s ? R and ? = min {r, s}, let D[x + r, x + s; ?n?1] ? ??n (x) be the divided difference of the functions ?n?1 = (?1)n ?(n?1) (n ?… read more here.
Keywords: monotonicity involving; complete monotonicity; divided difference; polygamma functions ... See more keywords
A complete monotonicity property of the multiple gamma function
Sign Up to like & getrecommendations! Published in 2020 at "Comptes Rendus Mathematique"
DOI: 10.5802/crmath.115
Abstract: We consider the following functions fn (x) = 1− ln x + lnGn (x +1) x and gn (x) = x Gn (x +1) x , x ∈ (0,∞), n ∈N, where Gn (z) =… read more here.
Keywords: complete monotonicity; completely monotonic; gamma function; function ... See more keywords