Suitable Algorithm Associated with a Parameterization for the Three-Parameter Log-Normal Distribution

Associated with a parameterization for the three-parameter lognormal distribution, an algorithm was proposed by Komori and Hirose, which can find a local maximum likelihood (ML) estimate surely if it exists. Nevertheless, by Vera and Díaz-García it was shown that performance in finding a local ML estimate deteriorated by adopting the parameterization only and using other algorithm. In the present article, it will be shown that Komori and Hirose’s algorithm should be used for the parameterization. This work will also give MATLAB codes as a useful tool for the parameter estimation of the distribution

On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Strong first order S-ROCK methods for stochastic differential equations

Explicit stochastic Runge–Kutta (SRK) methods are constructed for non-commutative Itô and Stratonovich stochastic differential equations. Our aim is to derive explicit SRK schemes of strong order one, which are derivative free and have large stability regions. In the present paper, this will be achieved by embedding Chebyshev methods for ordinary differential equations in SRK methods proposed by Rößler (2010). In order to check their convergence order, stability properties and computational efficiency, some numerical experiments will be performed

On the Integrability of Classical Ruijsenaars-Schneider Model of BC2BC_{2} Type

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found by solving the set of two functional equations.Comment: 10 pages, LaTeX2e, no figure