American Journal of Theoretical and Applied Statistics

Volume 6, Issue 5, September 2017

  • Marshall-Olkin Exponential Pareto Distribution with Application on Cancer Stem Cells

    Khairia El-Said El-Nadi, L. M. Fatehy, Nourhan Hamdy Ahmed

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 1-7
    Received: 8 December 2016
    Accepted: 27 December 2016
    Published: 24 January 2017
    DOI: 10.11648/j.ajtas.s.2017060501.11
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: A Marshall–Olkin variant of exponential Pareto distribution is being introduced in this paper. Some of its statistical functions and numerical characteristics among others characteristics function, moment generalizing function, central moments of real order are derived in the computational series expansion form and various illustrative special case... Show More
  • A Generalization of Some Lag Synchronization of System with Parabolic Partial Differential Equation

    Mahmoud M. El-Borai, Wagdy G. El-sayed., Aafaf E. Abduelhafid

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 8-12
    Received: 27 January 2017
    Accepted: 3 February 2017
    Published: 18 February 2017
    DOI: 10.11648/j.ajtas.s.2017060501.12
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: In this paper, we study generalized adaptive synchronization of Lorenz chaotic system with parabolic partial differential equation. Systems with three uncertain parameters and the non-linear adaptive feedback control technique are considered. Moreover, a systematic design process of parameters identification and Lag synchronization of chaotic syste... Show More
  • Solvability of Some Nonlinear Integral Functional Equations

    Mahmoud M. El-Borai, Wagdy G. El-Sayed, Noura N. Khalefa

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 13-22
    Received: 11 February 2017
    Accepted: 15 February 2017
    Published: 28 February 2017
    DOI: 10.11648/j.ajtas.s.2017060501.13
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: This paper discussed some existence theorems for nonlinear functional integral equations in the space L^1 of Lebesgue integrable functions,by using the Darbo fixed point theorem associated with the Hausdorff measure of noncompactness. Also, as an application, we discuss the existence of solutions for some nonlinear integral equations with fractiona... Show More
  • On Some Lag Synchronization and Higher Order Parabolic Systems

    Khairia El-Said El-Nadi, Wagdy G. Elsayed, Mabroka F. Bader

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 23-29
    Received: 7 March 2017
    Accepted: 8 March 2017
    Published: 20 March 2017
    DOI: 10.11648/j.ajtas.s.2017060501.14
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: Chaos synchronization is a topic of great interest, due to its observation in a huge variety of phenomena of different nature. We study synchronization of two chaotic oscillators in a Master- Slave configuration. The two dynamic systems are coupled via a directed feedback that randomly switches among a finite set of given constant function at a pre... Show More
  • Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations

    Mahmoud M. El-Borai, Wagdy G. Elsayed, Turkiya Alhadi Aljamal

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 30-39
    Received: 7 March 2017
    Accepted: 8 March 2017
    Published: 5 April 2017
    DOI: 10.11648/j.ajtas.s.2017060501.15
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: Novel equi-attractivity in large generalized non-linear partial differential equations were performed for the impulsive control of spatiotemporal chaotic. Attractive solutions of these general partial differential equations were determined. A proof for existence of a certain kind of impulses for synchronization such that the small error dynamics th... Show More
  • Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method

    Mahmoud M. El-borai, M. A. Abdou, E. M. Youssef

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 40-45
    Received: 20 March 2017
    Accepted: 21 March 2017
    Published: 5 April 2017
    DOI: 10.11648/j.ajtas.s.2017060501.16
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: In this paper, the Adomian decomposition method (ADM) is applied to obtain the approximate solution of a mathematical model of carcinogenesis which is a Riccati differential equation derived by Moolgavkar and Venzon (see [9]). The numerical solution obtained by this way have been compared with the exact solution which obtained by Moolgavkar and Ven... Show More
  • On The Fractional Optimal Control Problem with Free End Point

    Mahmoud M. El-borai, Wagdy G. ElSayed, M. A. Abdou, M. Taha E.

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 46-50
    Received: 15 March 2017
    Accepted: 16 March 2017
    Published: 11 April 2017
    DOI: 10.11648/j.ajtas.s.2017060501.17
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: We present a necessary optimality conditions for a class of optimal control problems. The dynamical control system involves integer and fractional order derivatives and the final time is free. Optimality conditions are obtained. Feedback control laws for linear dynamic system are obtained.
  • Evaluation of Techniques for Univariate Normality Test Using Monte Carlo Simulation

    Ukponmwan H. Nosakhare, Ajibade F. Bright

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 51-61
    Received: 24 February 2017
    Accepted: 1 March 2017
    Published: 9 June 2017
    DOI: 10.11648/j.ajtas.s.2017060501.18
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: This paper examines the sensitivity of nine normality test statistics; W/S, Jaque-Bera, Adjusted Jaque-Bera, D’Agostino, Shapiro-Wilk, Shapiro-Francia, Ryan-Joiner, Lilliefors’and Anderson Darlings test statistics, with a view to determining the effectiveness of the techniques to accurately determine whether a set of data is from normal distributio... Show More
  • Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation

    Ukponmwan H. Nosakhare, Ajibade F. Bright

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 62-65
    Received: 24 February 2017
    Accepted: 1 March 2017
    Published: 11 July 2017
    DOI: 10.11648/j.ajtas.s.2017060501.19
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: Among the test of normality in existence is the W/S which has standard table as the interval for critical region with both lower and upper bound. The test is suitable for sample size ranging from 3 as displayed in the W/S Critical table. But the sensitivity of the test can be determined by computation of power of the test which would show how sensi... Show More
  • Optimal Control of a Class of Parabolic Partial Fractional Differential Equations

    Mahmoud M. El-borai, Mohamed A. Abdou, Mai Taha Elsayed

    Issue: Volume 6, Issue 5-1, September 2017
    Pages: 66-70
    Received: 28 July 2017
    Accepted: 31 July 2017
    Published: 9 August 2017
    DOI: 10.11648/j.ajtas.s.2017060501.20
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    This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics
    Abstract: In this paper, the existence of the solution of the parabolic partial fractional differential equation is studied and the solution bound estimate which are used to prove the existence of the solution of the optimal control problem in a Banach space is also studied, then apply the classical control theory to parabolic partial differential equation i... Show More