Gwo Dong Lin
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View article: New Sufficient Conditions for Moment Determinacy via Probability Density Tails
New Sufficient Conditions for Moment Determinacy via Probability Density Tails Open
One of the ways to characterize a probability distribution is to show that it is moment-determinate, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends entirely on the behaviour of th…
View article: New Sufficient Conditions for Moment-determinacy via the Probability Density Tails
New Sufficient Conditions for Moment-determinacy via the Probability Density Tails Open
One of the ways to characterize a probability distribution is to show that it is moment-determinate, or, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends strongly on the behaviour o…
View article: EM Estimation of the B-Spline Copula with Penalized Pseudo-Likelihood Functions
EM Estimation of the B-Spline Copula with Penalized Pseudo-Likelihood Functions Open
The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. We develop a modified EM algorithm, to maximize the penalized pseudo-likelihood function, wherein we use the smoothly clipped abs…
View article: Integral Representations of Three Novel Multiple Zeta Functions for Barnes Type: A Probabilistic Approach
Integral Representations of Three Novel Multiple Zeta Functions for Barnes Type: A Probabilistic Approach Open
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 nu…
View article: New Characterizations of the Gamma Distribution via Independence of Two Statistics by Using Anosov's Theorem
New Characterizations of the Gamma Distribution via Independence of Two Statistics by Using Anosov's Theorem Open
Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other on…
View article: On the Semi-Mittag-Leffler Distributions
On the Semi-Mittag-Leffler Distributions Open
The semi-Mittag-Leffler (SML) distribution arises as the marginal of a stationary Markovian process, and is a generalization of the well-known Mittag-Leffler (ML) or positive Linnik distribution.Unlike the ML distribution, which has been w…
View article: Characterizations of the Normal Distribution via the Independence of the Sample Mean and the Feasible Definite Statistics with Ordered Arguments
Characterizations of the Normal Distribution via the Independence of the Sample Mean and the Feasible Definite Statistics with Ordered Arguments Open
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 …
View article: Characterizations of the Normal Distribution via the Independence of the\n Sample Mean and the Feasible Definite Statistics with Ordered Arguments
Characterizations of the Normal Distribution via the Independence of the\n Sample Mean and the Feasible Definite Statistics with Ordered Arguments Open
It is well known that the independence of the sample mean and the sample\nvariance characterizes the normal distribution. By using Anosov's theorem, we\nfurther investigate the analogous characteristic properties in terms of the\nsample me…
View article: An identity for two integral transforms applied to the uniqueness of a distribution via its Laplace–Stieltjes transform
An identity for two integral transforms applied to the uniqueness of a distribution via its Laplace–Stieltjes transform Open
It is well known that the Laplace-Stieltjes transform of a nonnegative random\nvariable (or random vector) uniquely determines its distribution function. We\nextend this uniqueness theorem by using the Muntz-Szasz Theorem and the\nidentity…
View article: Characterization of Probability Distributions via Functional Equations of Power-Mixture Type
Characterization of Probability Distributions via Functional Equations of Power-Mixture Type Open
We study power-mixture type functional equations in terms of Laplace–Stieltjes transforms of probability distributions on the right half-line [0,∞). These equations arise when studying distributional equations of the type Z=dX+TZ, where th…
View article: Characterization of Probability Distributions via Functional Equations of Power-Mixture Type
Characterization of Probability Distributions via Functional Equations of Power-Mixture Type Open
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…
View article: Necessary and Sufficient Conditions for Unique Solution to Functional Equations of Poincare Type
Necessary and Sufficient Conditions for Unique Solution to Functional Equations of Poincare Type Open
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 distribut…
View article: Dependence Properties of B-Spline Copulas
Dependence Properties of B-Spline Copulas Open
We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker's distributions. The range of correlation of the B-spline copulas is examined, and the Frechet--Hoeffding upper bound is prove…
View article: Absolute moments in terms of characteristic functions
Absolute moments in terms of characteristic functions Open
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 …