Approximations and inequalities for the exponential beta function
نویسندگان
چکیده
منابع مشابه
Exponential Models: Approximations for Probabilities
Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...
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Let g(x) := (e/x)xΓ(x+ 1) and F(x,y) := g(x)g(y)/g(x + y) . Let D x,y be the k th differential in Taylor’s expansion of logF(x,y) . We prove that when (x,y) ∈ R+ one has (−1)k−1D x,y (X ,Y ) > 0 for every X ,Y ∈ R+ , and that when k is even the conclusion holds for every X ,Y ∈ R with (X ,Y ) = (0,0) . This implies that Taylor’s polynomials for logF provide upper and lower bounds for logF accor...
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15 صفحه اولExponential Models: Approximations for Probabilities
Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property was and...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2019
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2208-2