American Journal of Applied Mathematics and Statistics

Seasonality accounts majorly for quarterly and monthly movements in macro-economics and time series and in modelling such patterns to have a forecasting robustness, precision and reliability have been steadily increased in recent years but no consensus has been reached as to which model yields the appropriate description. However, this research seeks to address the robustness and accuracy of seasonal ARIMA model of Naira/Dollar exchange rate using a monthly data for the period of Jan 1994 to July 2013. The series was subjected to a time plot revealing seasonal patterns and upward trend. Both behaviours were taken into account by moving average and seasonal moving average, where little or fewer months of data were used to estimate the local level and trend and also few seasons of data were averaged over to estimate the seasonal patterns. The proposed model shows predictive power, robustness and precision which was revealed by the normality of data and residual analysis. The estimated forecast values from our proposed model are more realistic and closely reflect in the current economic reality in two countries as indicated by the forecast measurement criteria.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 172-178. DOI: 10.12691/ajams-2-3-14
Pub. Date: June 18, 2014

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Recurrence Relations for Moments of k-th Upper Record Values from Flexible Weibull Distribution and a Characterization

by Mahmoud Ali Selim and Hamdy M. Salem

Original Research

In this paper, we establish some recurrence relations satisfied by single and product moments of k-th upper record values from the flexible Weibull distribution. We also give a characterization of flexible Weibull distribution by using the recurrence relations for single moments.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 168-171. DOI: 10.12691/ajams-2-3-13
Pub. Date: June 01, 2014

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Estimation of Population Total in the Presence of Missing Values Using a Modified Murthy's Estimator and the Weight Adjustment Technique

by Oyoo David Odhiambo and Christopher Ouma Onyango

Original Research

Use of Murthy’s method in estimation of population parameters, such as population totals, population means, and population variances has been limited to surveys where survey data values are complete. This study applies weight adjustment technique to estimate a population total under simple random sampling without replacement. The asymptotic properties show that the estimated population total is sufficient for the true population total. The proposed estimator is obtained by symmetrizing Murthy’s estimator.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 163-167. DOI: 10.12691/ajams-2-3-12
Pub. Date: May 29, 2014

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Inventory Management for Deteriorating Items with Salvage Value under Time Varying Demand Condition

by Srichandan Mishra, S.P. Mishra, N. Mishra, J. Panda and U.K. Misra

Original Research

In this paper we discuss the development of an inventory model for deteriorating items which investigates an instantaneous replenishment model for the items under cost minimization. The salvage value is incorporated to the deteriorated units. The result is illustrated with numerical example.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 160-162. DOI: 10.12691/ajams-2-3-11
Pub. Date: May 28, 2014

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A Theoretical Analysis for n-species Competition for Aphid Population in Limited Resources: A Modeling Study

by Rajan K Sharma, Shyam Sundar and D. Kandu

Original Research

In this paper, we have discussed a mathematical model for the competition in n-species aphid population for a limited resource and their limiting behavior is studied as time approaches to infinity. Aphids are among the most conspicuous and important pests in green houses and crops. It is assumed that aphids excrete honeydew and cover an area

by it’s saliva at time

which then form a weak cover on the leaf surface preventing the individuals from further sucking and movement and therefore causing deaths due to starvation. It means that the mortality rate of aphids become very high in the environment by honeydew excretions of other aphids. Analytically, it has been shown that how aphid population grows with time

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 157-159. DOI: 10.12691/ajams-2-3-10
Pub. Date: May 21, 2014

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On Optimal Weighting Scheme in Model Averaging

by Georges Nguefack-Tsague

Original Research

Model averaging is an alternative to model selection and involves assigning weights to different models. A natural question that arises is whether there is an optimal weighting scheme. Various authors have shown their existence in others methodological frameworks. This paper investigates the derivation of optimal weights for model averaging using square error loss. It is shown that though these weights may exist in theory and depend on model parameters; once estimated they are no longer optimal. It is demonstrated using an example of linear regression that model averaging estimators with these estimated weights are unlikely to outperform post-model selection and others model averaging estimators. We provide a theoretical justification for this phenomenon.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 150-156. DOI: 10.12691/ajams-2-3-9
Pub. Date: May 20, 2014

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Darcy’s Law Equation with Application to Underground Seepage in Earth Dams in Calculation of the Amount of Seepage

by Koros Kiplangat Vincent, Mutua Nicholas Muthama and Sakayo Nicodemus Muoki

Original Research

Water is a very important natural resource that no creation can exist without it. Hence it has become a responsibility of every person to try and conserve this very precious resource. One of the ways of conservation is by building earth dams. However if they are not well managed these dams may end up drying up due to underground seepage leading to failure of the dam. In this paper we are concerned with how to calculate the discharge rate through a porous medium, the velocity of the discharge and finally the total discharge using Darcy’s law. This study will also describe a computer based model that accepts input and calculate the amount of discharge per given time. From Darcy’s law it is shown that, the discharge rate depends among other factors the porosity of the medium. So from the study we were able to determine which medium is able to hold water rather than supporting percolation.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 143-149. DOI: 10.12691/ajams-2-3-8
Pub. Date: May 16, 2014

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Various Numerical Methods for Singularly Perturbed Boundary Value Problems

by Hradyesh Kumar Mishra and Sonali saini

Review Article

The numerical treatment of singular perturbation problems is currently a field in which active research is going on these days. Singular perturbation problems in which the term containing the highest order derivative is multiplied by a small parameter ε, occur in a number of areas of applied mathematics, science and engineering among them fluid mechanics (boundary layer problems) elasticity (edge effort in shells) and quantum mechanics. In this paper, we consider few numerical methods for singularly perturbed boundary value problems developed by numerous researchers between 2006 to 2013. A Summary of the result of some recent methods is presented and this leads to conclusion and recommendations regarding methods to use on singular perturbation problem.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 129-142. DOI: 10.12691/ajams-2-3-7
Pub. Date: May 16, 2014

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Inference on P(X < Y) for Extreme Values

by Sudhansu S. Maiti and Sudhir Murmu

Original Research

The article considers the problem of

, when X and Y belong to independently distributed two extreme value distributions. Maximum likelihood estimate of R has been found out and the estimates assuming different distributions have been compared for complete samples. Lower confidence limits of R have been found out by Delta method and bootstrap method. The Bayes estimate of R has also been calculated using MCMC approach.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 121-128. DOI: 10.12691/ajams-2-3-6
Pub. Date: May 10, 2014

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20495 Views6419 Downloads33 Likes

Assessing the Players’ Performance in the Game of Bridge: A Fuzzy Logic Approach

by Michael Gr. Voskoglou

Original Research

Contract bridge occupies nowadays a position of great prestige being, together with chess, the only mind sports officially recognized by the International Olympic Committee. In the present paper an innovative method for assessing the total performance of bridge-players’ belonging to groups of special interest (e.g. different bridge clubs during a tournament, men and women, new and old players, etc) is introduced, which is based on principles of fuzzy logic. For this, the cohorts under assessment are represented as fuzzy subsets of a set of linguistic labels characterizing their performance and the centroid defuzzification method is used to convert the fuzzy data collected from the game to a crisp number. This new method of assessment could be used informally as a complement of the official bridge-scoring methods for statistical and other obvious reasons. Two real applications related to simultaneous tournaments with pre-dealt boards, organized by the Hellenic Bridge Federation, are also presented, illustrating the importance of our results in practice.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 115-120. DOI: 10.12691/ajams-2-3-5
Pub. Date: May 01, 2014

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Application of Homotopy Analysis Method in One-Dimensional Instability Phenomenon Arising in Inclined Porous Media

by Kajal K. Patel, M. N. Mehta and Twinkle R. Singh

Original Research

During secondary oil recovery process when water is injected in inclined oil formatted area then phenomenon of instability occurs due to viscosity difference of water and oil. The non-linear partial differential equation for this instability phenomenon have been obtained. The Homotopy analysis method has been applied to this governing equation by using appropriate initial and boundary conditions. The guess value of saturation of injected water has been satisfying its initial and boundary conditions. The numerical value and graphical presentation are given by using Maple software and it is concluded that the saturation of injected water is increasing during instability phenomenon in inclined porous media when length of fingers and time increases.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 106-114. DOI: 10.12691/ajams-2-3-4
Pub. Date: May 01, 2014

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Application of Haar Wavelets and Method of Moments for Computing Performance Characteristics of Electromagnetic Materials

by Vishwa Nath Maurya and Avadhesh Kumar Maurya

Original Research

Present paper demonstrates on application aspect of Haar wavelets and method of moments for computing performance characteristics in electromagnetic field. In this paper, some significant results including performance characteristics relevant to application of the Haar wavelets as the expansion function in the method of moments have been successfully explored. The present analysis for performance evaluation has been focused for three different electromagnetic materials- finite straight, thin plane plate and eddy current problem. The main results explored are described in the main text and also concluded at the end with discussions.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 96-105. DOI: 10.12691/ajams-2-3-3
Pub. Date: April 27, 2014

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Testing the Consistency of Subjective Weights in Goal Programming – the Analytical Hierarchy Process Approach

by T. Ganesh and PRS Reddy

Original Research

In the context of multi-criteria decision making every individual will act as a decision maker. The decision maker is involved in assigning preferences or weights to the alternatives. Goal programming will also come under the hub of MCDA, where the DM will assign the subjective weights to each goal. By giving so, the weighted sum of deviations will be minimized to some extent but one cannot ascertain whether the weights are consistent or not. In this paper the authors have proposed a simpler way of testing the consistency of weights and demonstrated an easier way to achieve the minimized weighted sum of deviations through AHP. This attempt showed better results and allows the DM to think well before giving the weights to each goal.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 92-95. DOI: 10.12691/ajams-2-3-2
Pub. Date: April 23, 2014

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Unique Lacunary interpolations with Estimate Errors Bound

by Faraidun K. HamaSalh and Shko A. Tahir

Original Research

This paper presents a formulation of a Lacunary approximation for the class ninth of spline function at uniform mesh points and the function values at the end points of the interval. Error bounds for the function and its derivatives are derived. Finally, efficiency estimation and convergence orders are also illustrate errors derivations.

American Journal of Applied Mathematics and Statistics. 2014, 2(3), 88-91. DOI: 10.12691/ajams-2-3-1
Pub. Date: April 07, 2014

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13550 Views4334 Downloads34 Likes