In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this generalization and derive new inequalities involving ratios of multivariate gamma functions.Comment: 12 pages, 0 figure
In the paper, three basic properties of the logarithmically N-alternating monotonic functions are e...
In the paper, three basic properties of the logarithmically N-alternating\ud monotonic functions are...
Abstract In this paper, by using the properties of an auxiliary function, we mainly present the nece...
Abstract In the paper, the authors concisely survey and review some func-tions involving the gamma f...
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonic...
A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that ea...
In the article, some strictly Logarithmically completely monotonic ratios of mean values are presen...
AbstractWe present some complete monotonicity and logarithmically complete monotonicity properties f...
In the article, the logarithmic mean is proved to be completely monotonic and an open problem about...
For a non-negative continuous random variable , Chaudhry and Zubair (2002, p. 19) introduced a proba...
We give an infinite family of functions involving the gamma function whose logarithmic derivatives a...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
In the article, the logarithmic mean is proved to be completely\ud monotonic and an open problem abo...
In the paper, three basic properties of the logarithmically N-alternating monotonic functions are e...
In the paper, three basic properties of the logarithmically N-alternating\ud monotonic functions are...
Abstract In this paper, by using the properties of an auxiliary function, we mainly present the nece...
Abstract In the paper, the authors concisely survey and review some func-tions involving the gamma f...
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonic...
A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that ea...
In the article, some strictly Logarithmically completely monotonic ratios of mean values are presen...
AbstractWe present some complete monotonicity and logarithmically complete monotonicity properties f...
In the article, the logarithmic mean is proved to be completely monotonic and an open problem about...
For a non-negative continuous random variable , Chaudhry and Zubair (2002, p. 19) introduced a proba...
We give an infinite family of functions involving the gamma function whose logarithmic derivatives a...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
In the article, the logarithmic mean is proved to be completely\ud monotonic and an open problem abo...
In the paper, three basic properties of the logarithmically N-alternating monotonic functions are e...
In the paper, three basic properties of the logarithmically N-alternating\ud monotonic functions are...
Abstract In this paper, by using the properties of an auxiliary function, we mainly present the nece...
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