Science Journal of Applied Mathematics and Statistics

Volume 4, Issue 6, December 2016

  • Estimating the Extreme Financial Risk of the Kenyan Shilling Versus Us Dollar Exchange Rates

    Charles Kithenge Chege, Joseph Kyalo Mungat’u, Oscar Ngesa

    Issue: Volume 4, Issue 6, December 2016
    Pages: 249-255
    Received: 1 September 2016
    Accepted: 23 September 2016
    Published: 14 October 2016
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    Abstract: In the last decade, world financial markets, including the Kenyan market have been characterized by significant instabilities. This has resulted to criticism on available risk management systems and motivated research on better methods capable of identifying rare events that have resulted in heavy consequences. With the high volatility of the Kenya... Show More
  • Statistical Models for Count Data

    Alexander Kasyoki Muoka, Oscar Owino Ngesa, Anthony Gichuhi Waititu

    Issue: Volume 4, Issue 6, December 2016
    Pages: 256-262
    Received: 13 September 2016
    Accepted: 23 September 2016
    Published: 15 October 2016
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    Abstract: Statistical analyses involving count data may take several forms depending on the context of use, that is; simple counts such as the number of plants in a particular field and categorical data in which counts represent the number of items falling in each of the several categories. The mostly adapted model for analyzing count data is the Poisson mod... Show More
  • Option Pricing under Delay Geometric Brownian Motion with Regime Switching

    Tianyao Fang, Liangjian Hu, Yun Xin

    Issue: Volume 4, Issue 6, December 2016
    Pages: 263-268
    Received: 18 October 2016
    Published: 19 October 2016
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    Abstract: We investigate the option pricing problem when the price dynamics of the underlying risky assets are driven by delay geometric Brownian motions with regime switching. That is, the market interest rate, the appreciation rate and the volatility of the risky assets depend on the past stock prices and the unobservable states of the economy which are mo... Show More
  • The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface

    Magomed Farman Mekhtiyev, Nina Ilyinichna Fomina, Nazaket Boyukaga Mammadova

    Issue: Volume 4, Issue 6, December 2016
    Pages: 269-275
    Received: 23 September 2016
    Accepted: 7 October 2016
    Published: 3 November 2016
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    Abstract: The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the ... Show More
  • The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching

    Juan Hou, Yanqun Wang, Zhenguo Luo

    Issue: Volume 4, Issue 6, December 2016
    Pages: 276-283
    Received: 30 September 2016
    Accepted: 13 October 2016
    Published: 7 November 2016
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    Abstract: In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.
  • Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values

    Lanping Li

    Issue: Volume 4, Issue 6, December 2016
    Pages: 284-288
    Received: 9 October 2016
    Accepted: 20 October 2016
    Published: 14 November 2016
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    Abstract: This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal proba... Show More
  • Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model

    Stephen Muthii Wanjohi, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya

    Issue: Volume 4, Issue 6, December 2016
    Pages: 289-297
    Received: 4 October 2016
    Accepted: 25 October 2016
    Published: 16 November 2016
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    Abstract: Extreme value theory is the study of extremal properties of random processes, it models and measures events that occur with little probability. The extreme value theory is a robust framework to analyze the tail behavior of distributions. It has been applied extensively in hydrology, climatology, insurance and finance industry. The information of pr... Show More
  • Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations

    Xiufeng Guo

    Issue: Volume 4, Issue 6, December 2016
    Pages: 298-302
    Received: 4 November 2016
    Accepted: 25 November 2016
    Published: 14 December 2016
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    Abstract: In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boun... Show More