American Journal of Applied Mathematics and Statistics

The proposed work is devoted to the use of the Bayesian approach based on probabilistic method of use, along with the original statistical data prior information about the current process. Especially significant advantages over classical methods in terms of the accuracy of the statistical inference Bayesian approach is in the relatively small samples, which is very characteristic of the simulation. A theorem on minimizing classification error probability is proved. About choosing a priori distribution parameters from the coordinated class of distributions is considered.

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 257-262. DOI: 10.12691/ajams-3-6-7
Pub. Date: December 02, 2015

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A Boundary Value Problem for the Equation of Motion of a Homogeneous Bar with Periodic Conditions

by Elvin I. Azizbayov and Yashar T. Mehraliyev

Original Research

In this paper the classical solution of a nonlocal boundary value problem for the equation of motion of a homogeneous bar is investigated. Then using Fourier’s method stated problem reduced to an integral equation. Further, exploiting the contracting mappings principle the existence and uniqueness of the classical solution for the considered boundary value problem is proved

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 252-256. DOI: 10.12691/ajams-3-6-6
Pub. Date: November 27, 2015

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Modification of the Sandwich Estimator in Generalized Estimating Equations with Correlated Binary Outcomes in Rare Event and Small Sample Settings

by Paul Rogers and Julie Stoner

Original Research

Regression models for correlated binary outcomes are commonly fit using a Generalized Estimating Equations (GEE) methodology. GEE uses the Liang and Zeger sandwich estimator to produce unbiased standard error estimators for regression coefficients in large sample settings even when the covariance structure is misspecified. The sandwich estimator performs optimally in balanced designs when the number of participants is large, and there are few repeated measurements. The sandwich estimator is not without drawbacks; its asymptotic properties do not hold in small sample settings. In these situations, the sandwich estimator is biased downwards, underestimating the variances. In this project, a modified form for the sandwich estimator is proposed to correct this deficiency. The performance of this new sandwich estimator is compared to the traditional Liang and Zeger estimator as well as alternative forms proposed by Morel, Pan and Mancl and DeRouen. The performance of each estimator was assessed with 95% coverage probabilities for the regression coefficient estimators using simulated data under various combinations of sample sizes and outcome prevalence values with an Independence (IND), Autoregressive (AR) and Compound Symmetry (CS) correlation structure. This research is motivated by investigations involving rare-event outcomes in aviation data.

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 243-251. DOI: 10.12691/ajams-3-6-5
Pub. Date: November 22, 2015

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Asymptotic Solutions of Fifth Order More Critically Damped Nonlinear Systems in the Case of Four Repeated Roots

by M. Abul Kawser, Md. Mahafujur Rahaman, Md. Shajib Ali and Md. Nurul Islam

Original Research

In this article, we have modified the Krylov-Bogoliubov-Mitropolskii (KBM) method, which is one of the most widely used methods to delve into the transient behavior of oscillating systems, to find out the solutions of fifth order more critically damped nonlinear systems. In this paper, we have considered the asymptotic solutions of fifth order more critically damped nonlinear systems when the four eigenvalues are equal and another one is distinct. This article suggests that the perturbation solutions obtained by the modified KBM method for both the cases (when repeated eigenvalues are greater than the distinct eigenvalue, and when the distinct eigenvalue is greater than repeated eigenvalues) satisfactorily correspond to the numerical solutions obtained by Mathematica 9.0.

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 233-242. DOI: 10.12691/ajams-3-6-4
Pub. Date: November 16, 2015

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A Fixed Point Approach to Hyers-Ulam-Rassias Stability of Nonlinear Differential Equations

by Maher Nazmi Qarawani

Original Research

In this paper we use the fixed point approach to obtain sufficient conditions for Hyers-Ulam-Rassias stability of nonlinear differential. Some illustrative examples are given.

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 226-232. DOI: 10.12691/ajams-3-6-3
Pub. Date: November 05, 2015

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Derivation of Continuous Linear Multistep Methods Using Hermite Polynomials as Basis Functions

by T. Aboiyar., T. Luga. and B.V. Iyorter

Original Research

This paper concerns the derivation of continuous linear multistep methods for solving first-order initial value problems (IVPs) of ordinary differential equations (ODEs) with step number k=3 using Hermite polynomials as basis functions. Adams-Bashforth, Adams-Moulton and optimal order methods are derived through collocation and interpolation technique. The derived methods are applied to solve two first order initial value problems of ordinary differential equations. The result obtained by the optimal order method compared favourably with those of the standard existing methods of Adams-Bashforth and Adams-Moulton.

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 220-225. DOI: 10.12691/ajams-3-6-2
Pub. Date: October 29, 2015

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Boundary Layer Stagnation-Point Flow of Second Grade Fluid over an Exponentially Stretching Sheet

by Abdul Rehman, Ghulam Farooq, Israr Ahmed, Muhammad Naseer and Muhammad Zulfiqar

Original Research

In this paper, the steady boundary layer stagnation point flow and heat transfer of a second grade fluid over an exponentially stretching sheet is investigated. The solutions are obtained through homotopy analysis method (HAM) and the Keller-box technique. Comparisons of both the solutions are given graphically as well as in tabular form. The effects of second grade parameter β Prandtl number Pr and other important physical parameters are presented through graphs and the salient features are discussed.

American Journal of Applied Mathematics and Statistics. 2015, 3(6), 211-219. DOI: 10.12691/ajams-3-6-1
Pub. Date: October 28, 2015

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