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Vol 53, No 3 (2018)
- Year: 2018
- Articles: 9
- URL: https://journals.rcsi.science/1068-3623/issue/view/14084
Differential Equations
Comparison of the Strengths of Polynomials of Two Variables
Abstract
In this paper, for homogeneous polynomials of two variables we find necessary and sufficient conditions for comparison of the weighted strengths of these polynomials. The conditions are stated in terms of orders and multiplicities of the zeros of the considered polynomials.
121-127
Real and Complex Analysis
128-133
On a Class of L-Wiener-Hopf Operators
Abstract
By replacement in the definition of the convolution operator of Fourier transform by a spectral transform of a selfadjoint Sturm-Liouville operator on the axis L, the concepts of Lconvolution and L-Wiener-Hopf operators are introduced. The case of the reflectorless potentials with a single eigenvalue is considered. A relationship between the Wiener-Hopf and L-Wiener- Hopf operators is established. In the case of piecewise continuous symbol the Fredholm property and invertibility of the L-Wiener-Hopf operator are investigated.
134-138
On an Analog of the Plan’s Formula
Abstract
In this paper we obtain an analog of the Plan’s formula, which plays an essential role in obtaining a functional relation for classical Riemann zeta-function.We provide examples of rational functions that satisfy a certain symmetry condition and admit a Maclaurin series expansion with coefficients equal to zero or one.
139-146
Generalized Characteristics for Meromorphic in the Half-plane Functions
Abstract
In this paper we introduce generalized characteristics for meromorphic in the halfplane functions, and generalize the Levin’s formula and the first fundamental theorem for Tsuji’s characteristics.
147-152
On an Interpolation by the Modified Trigonometric System
Abstract
We consider interpolations by the modified trigonometric system and explore convergence in different frameworks.We prove better convergence of such interpolations for odd functions compared to the interpolations with the classical trigonometric system.
153-161
Probability Theory and Mathematical Statistics
On the Parameters Estimators for a Discrete Analog of the Generalized Exponential Distribution
Abstract
Nekoukhou et. al (Commun. Statist. Th. Meth., 2012) introduced a two-parameters discrete probability distribution so-called Discrete Analog of the Generalized Exponential Distribution (in short, DGED). We shall attempt to derive conditions under which a solution for the system of likelihood equations exists and coincides with the maximum likelihood (ML) estimators of the DGED. This kind of ML estimators are coincided with some moment estimators. An approximate computation based on Fisher’s accumulation method is presented in order for the ML estimations of the unknown parameters. Simulation study is also illustrated. Meanwhile, in the sequel two special cases of the DGED are considered. Some statistical properties for such special cases of the DGED are provided. We also propose a linear regression-type model for estimation of the parameter. Finally, we fit the DGED to a real data set and compare it with two other discrete distributions.
162-171
Goodness-of-fit Tests for Continuous-time Stationary Processes
Abstract
The paper considers the following problem of hypotheses testing: based on a finite realization {X(t)}, 0 ≤ t ≤ T of a zero mean real-valued mean square continuous stationary Gaussian process X(t), t ϵ R, construct goodness-of-fit tests for testing a hypothesis H0 that the hypothetical spectral density of the process X(t) has the specified form. We show that in the case where the hypothetical spectral density of X(t) does not depend on unknown parameters (the hypothesis H0 is simple), then the suggested test statistic has a chi-square distribution. In the case where the hypothesis H0 is composite, that is, the hypothetical spectral density of X(t) depends on an unknown p–dimensional vector parameter, we choose an appropriate estimator for unknown parameter and describe the limiting distribution of the test statistic, which is similar to that of obtained by Chernov and Lehman in the case of independent observations. The testing procedure works both for short- and long-memory models.
172-179
The Distribution of the Maximum, Minimum and Range of a Sample
Abstract
The range of a sample is the difference between the maximum and minimum values. The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. In futures market commonly it is given daily high, low, open and close prices data. In this paper we take high and low prices and find what distribution will fit them better.
180-186