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74 research outputs found

On approximating the distribution of indefinite quadratic expressions in singular normal vectors

Author: Mohsenipour Akbar
Provost Serge B.
Publication venue: 'University of Tartu'
Publication date: 31/12/2011
Field of study

General representations of quadratic forms and quadratic expressions in singular normal vectors are given in terms of the difference of two positive definite quadratic forms and an independentlydistributed linear combination of normal random variables. Up to now, only special cases have been treated in the statistical literature. The densities of the quadratic forms are then approximated with gamma and generalized gamma density functions. A moment-based technique whereby the initial approximations are adjusted by means of polynomials is presented. Closed form and integral formulae are provided for the approximate density functions of the quadratic forms and quadratic expressions. A detailed step-by-step algorithm for implementing the proposed density approximation technique is also provided. Two numerical examples illustrate the methodology

Journals from University of Tartu

Polynomial expansions via embedded Pascal’s triangles

Author: Provost Serge B.
Ratemi Wajdi M.
Publication venue: 'University of Tartu'
Publication date: 31/12/2011
Field of study

An expansion is given for polynomials of the form (ω + λ1) · · ·(ω +λn). The coefficients of the resulting polynomials are related to their roots, and a system of equations that enables one to numericallydetermine the roots in terms of the coefficients is specified. The case where all the roots λi are equal is considered as well. A multinomial extension to polynomials of the form (x1+ · · · + xI )n is then provided. As it turns out, the coefficients of the monomials contained in the resulting polynomial expansion can be determined in terms of the coefficients of the monomials included in the expansion of (x1+ · · · + xI-1 )n  and the rows of embedded Pascal’s triangles of successive orders. An algorithm is provided for generating and concatenating these rows, with the particulars of its implementation by means of the symbolic computation software Mathematica being discussed as well. Potential applications of such expansions to combinatorics and genomics are also suggested

Journals from University of Tartu

On the Distribution of the Peña Rodríguez Portmanteau Statistic

Author: Deepak Sanjel
Serge B. Provost
Susan Z. Sheng
Publication venue: 'Pakistan Journal of Statistics and Operation Research'
Publication date: 01/07/2012
Field of study

<p class="MsoNormal" style="text-align: justify;"><span style="font-size: 10pt;">Peña and Rodríguez (2002) introduced a portmanteau test for time series which turns out to be more powerful than those proposed by Ljung and Box (1986) and Monti (1994), and approximated its distribution by means of a two-parameter gamma random variable. A polynomially adjusted beta approximation is proposed in this paper. This approximant is based on the moments of the statistic, which can be estimated by simulation or determined by symbolic computations or numerical integration. Various types of time series processes such as AR(1), MA(1), ARMA<span>(2,2) </span>are being considered. The proposed approximation turns out to be nearly exact.</span></p

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Directory of Open Access Journals

Pakistan Journal of Statistics and Operation Research

Effects of Transceiver Jitter on the Performance of Optical Scattering Communication Systems

Author: Ma Jianshe
Provost Serge B.
Shen Zanqiu
Su Ping
Publication venue
Publication date: 02/02/2024
Field of study

In ultraviolet communications, the transceiver jitter effects have been ignored in previous studies, which can result in non-negligible performance degradation especially in vibration states or in mobile scenes. To address this issue, we model the relationship between the received power and transceiver jitter by making use of a moment-based density function approximation method. Based on this relationship, we incorporate the transceiver jitter effects in combination with Poisson distribution. The error rate results are obtained assuming on-off key modulation with optimal threshold based detection. We validate the error rate expressions by comparing the analytical results with Monte-Carlo simulation results. The results show that the transceiver jitter effects cause performance degradation especially in smaller transceiver elevation angles or in shorter distances, which are often adopted in short-range ultraviolet communications. The results also show that larger elevation angle cases have a better performance with respect to anti-jitter and may perform better compared to smaller elevation angle situations in the case of larger standard deviation of jitter. This work studies for the first time the transceiver jitter effects in ultraviolet communications and provides guidelines for experimental system design.Comment: 5 pages, 2 figures, comments are welcome

arXiv.org e-Print Archive

Multivariate Statistical Analysis in the Real and Complex Domains

Author: Haubold Hans J.
Mathai Arak M.
Provost Serge B.
Publication venue: 'Springer Science and Business Media LLC'
Publication date: 18/11/2022
Field of study

This book explores topics in multivariate statistical analysis, relevant in the real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also contains original results, with the goal of driving research conversations forward. This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Numerous exercises are included throughout

Directory of Open Access Books (DOAB)

Multivariate time series modeling of monthly rainfall amounts

Author: Mahdi Esam
Nashwan Imad I. H.
Provost Serge B.
Salha Raid B.
Publication venue: Coordinamento SIBA - Università del Salento
Publication date: 26/04/2017
Field of study

This paper discusses the tting of suitable models to rainfall observations.Daily rainfall amounts were aggregated to monthly data using the Thiessenpolygons method and multivariate seasonal vector integrated autoregressivemoving average models (sVARIMA) were tted to the monthly cumulative rainfall volume. The data were obtained from the 12 Palestinian meteorological gauge stations located across the 5 governorates of the Gaza Strip and incorporated 42 years (from 1973 to 2014) of irregular daily precipitation. It can be concluded that the use of sVARIMAmodels in the environmental science provide a useful method to forecast rainfall data as a preliminary guideline for short and long-term sustainable water resources management

ESE - Salento University Publishing

Università del Salento: ESE - Salento University Publishing