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Chin-Yuan Hu

Publications and source records attributed to Chin-Yuan Hu.

8 recordsLinked to original sources
arXiv2026

Integral Representations of Three Novel Multiple Zeta Functions for Barnes Type: A Probabilistic Approach

Integral representation is one of the powerful tools for studying analytic continuation of the zeta functions. It is known that Hurwitz zeta function generalizes the famous Riemann zeta function which plays an important role in analytic number theory. They both have several multiple versions in the literature. In this paper, we introduce three novel multiple zeta functions for Barnes type and study their integral representations through hyperbolic probability distributions given by Pitman and Yor(Canad. J. Math., 55 (2003), 292--330). The analytically continued properties of the three multiple zeta functions are also investigated. The first one generalizes the well-known Barnes multiple zeta function, while the second and the third, unlike the previous results, can extend analytically to entire functions in the whole complex plane. These are somewhat surprising results.

math.NT↗
arXiv2022

The Best Bounds for Range Type Statistics

In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.

math.PR↗
arXiv2021

Characterizations of the Normal Distribution via the Independence of the Sample Mean and the Feasible Definite Statistics with Ordered Arguments

It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean and some feasible definite statistics. The latter statistics introduced in this paper for the first time are based on nonnegative, definite and continuous functions of ordered arguments with positive degree of homogeneity. The proposed approach seems to be natural and can be used to derive easily characterization results for many feasible definite statistics, such as known characterizations involving the sample variance, sample range as well as Gini's mean difference.

math.ST↗
arXiv2020

Characterization of Probability Distributions via Functional Equations of Power-Mixture Type

We study power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions. These equations arise when studying distributional equations of the type Z = X + TZ, where T is a known random variable, while the variable Z is defined via X, and we want to `find' X. We provide necessary and sufficient conditions for such functional equations to have unique solutions. The uniqueness is equivalent to a characterization property of a probability distribution. We present results which are either new or extend and improve previous results about functional equations of compound-exponential and compound-Poisson types. In particular, we give another affirmative answer to a question posed by J. Pitman and M. Yor in 2003. We provide explicit illustrative examples and deal with related topics.

math.PR↗
arXiv2020

Necessary and Sufficient Conditions for Unique Solution to Functional Equations of Poincare Type

Distributional equation is an important tool in the characterization theory because many characteristic properties of distributions can be transferred to such equations. Using a novel and natural approach, we retreat a remarkable distributional equation whose corresponding functional equation in terms of Laplace-Stieltjes transform is of the Poincare type. The necessary and sufficient conditions for the equation to have a unique distributional solution with finite variance are provided. This complements the previous results which involve at most the mean of the distributional solution. Besides, more general distributional (or functional) equations are investigated as well.

math.PR↗
arXiv2018

Absolute moments in terms of characteristic functions

The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the characteristic function (which have been ignored in the literature) and provide some new results as well. The case of nonnegative random variables is also investigated through both characteristic function and Laplace-Stieltjes transform. Besides, we prove that the distribution of a nonnegative random variable with a finite fractional moment can be completely determined by a proper subset of the translated fractional moments. This improves significantly P. Hall's (1983, Z. W., Vol. 62, 355-359) result for distributions on the right-half line.

math.PR↗
arXiv2018

Characterizations of the Logistic and Related Distributions

It is known that few characterization results of the logistic distribution were available before, although it is similar in shape to the normal one whose characteristic properties have been well investigated. Fortunately, in the last decade, several authors have made great progress in this topic. Some interesting characterization results of the logistic distribution have been developed recently. In this paper, we further provide some new results by the distributional equalities in terms of order statistics of the underlying distribution and the random exponential shifts. The characterization of the closely related Pareto type II distribution is also investigated.

math.ST↗