American Journal of Applied Mathematics and Statistics

Considering a natural model of systematic sampling, we can calculate the expectation of statistic exactly as it is without regarding it as any other sampling methods. I will demonstrate the details of calculation and get some results. It can be shown that the sample mean of systematic sampling is an unbiased estimator of population mean. Variance of sample mean can be described explicitly and depends on how to sort a population list. Sum of the variance of sample mean and the mean of sample variance is kept constant between random and systematic sampling. As the sample size becomes larger, the variance of sample mean converges to 0.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 344-351. DOI: 10.12691/ajams-2-5-8
Pub. Date: October 22, 2014

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Numerical Solution of Singularly Perturbed Differential-Difference Equations with Dual Layer

by Lakshmi Sirisha and Y.N. Reddy

Original Research

In this paper, we discuss the numerical solution of singularly perturbed differential-difference equations exhibiting dual layer behavior. First the second order singularly perturbed differential-difference equation is replaced by an asymptotically equivalent second order singularly perturbed ordinary differential equation. Then, second order stable central difference scheme has been applied to get a three term recurrence relation which is easily solved by Discrete Invariant Imbedding Algorithm. Some numerical examples have been considered to validate the computational efficiency of the proposed numerical scheme. To analyze the effect of the parameters on the solutions, the numerical solutions have also been plotted using graphs. The error bound and convergence of the method have also been established.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 336-343. DOI: 10.12691/ajams-2-5-7
Pub. Date: October 19, 2014

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Recurrence Relations for Single and Product Moments of Generalized Order Statistics from Left Truncated Logistic Distribution

by Kamal Nain Kapoor

Original Research

In this paper, we establish some recurrence relations satisfied by single and product moments of Generalized Order Statistics from Left Truncated Logistic Distribution. These recurrence relations are independent of left truncated point and therefore are also applicable for Logistic as well as for half Logistic distributions studied in Balakrishnan (1985) and Saran and Pandey (2012). For a particular case these results verify the corresponding results of Saran and Pandey (2004) and Kumar (2010) for p=∞.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 330-335. DOI: 10.12691/ajams-2-5-6
Pub. Date: October 04, 2014

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Recurrence Relations for Moments of Generalized Order Statistics from Marshall – Olkin extended Kumaraswamy distribution and its Characterization

by Ibrahim B. Abdul-Moniem

Original Research

In this paper, Marshall – Olkin extended Kumaraswamy distribution will be obtained. We give some properties for this distribution. Recurrence relations for single and product moments of generalized order statistics from Marshall – Olkin extended Kumaraswamy distribution have been obtained. Specializations to order statistics and records have been made. Further, using a recurrence relation for single moments we obtain characterization of Marshall – Olkin extended Kumaraswamy distribution.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 324-329. DOI: 10.12691/ajams-2-5-5
Pub. Date: October 01, 2014

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Transportation Algorithm with Volume Discount on Distribution Cost (A Case Study of the Nigerian Bottling Company Plc Owerri Plant)

by OSUJI GEORGE A., OGBONNA CHUKWUDI J. and OPARA JUDE

Original Research

This study is focused on the Application of Transportation Algorithm with volume Discount on distribution cost using Nigerian Bottling Company Plc Owerri Plant. This paper is intended to determine the quantity of Fanta (in crates), Coke (in crates) and Sprite (also in crates) that the Company should distribute in a month in order to minimize transportation cost and maximize profit. A problem of this nature was identified as a Nonlinear Transportation Problem (NTP), formulated in mathematical terms and solved by the Karush-Kuhn-Tucker (KKT) optimality condition for the NTP. A statistical software package was used to obtain the initial basic feasible solution using the Least Cost Method. Thus, analysis revealed that the optimal solution that gave minimum achievable cost of supply was the supply of 5000 crates of Fanta and 6000 crates of the same product to Umuahia market zone and Afikpo respectively. 7000 crates of Coke, 9000 crates and 1000 crates of the same product should be supplied to Orlu, Mbaise, and Afikpo market zones respectively. 6000, and 5000 crates of Sprite should be allocated to Mbaise and Umuahia market zones respectively, at a total cost of N377, 000.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 318-323. DOI: 10.12691/ajams-2-5-4
Pub. Date: September 29, 2014

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Application of Inventory Model in Determining Stock Control in an Organization

by Hycinth Chukwudi Iwu, Chukwudi J. Ogbonna, Opara Jude and Kalu Georgina Onuma

Original Research

This paper investigates the application of inventory model in determining stock control in an organization. A multi-product Economic Order Quantity model was used to determine the optimal order times. The result of the analysis revealed that J.O. Adimoha's investment does not have a proper inventory management which leads them to sometimes either over stock or under stock. The combination of orders at different time interval was carefully and constantly updated and verified because reorder points and EOQ may change. In conclusion, it was discovered that reorder points often coincides close together.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 307-317. DOI: 10.12691/ajams-2-5-3
Pub. Date: September 28, 2014

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One Modulo Three Mean Labeling of Graphs

by P. Jeyanthi and A. Maheswari

Original Research

In this paper, we introduce a new labeling called one modulo three mean labeling. A graph G is said to be one modulo three mean graph if there is an injective function

from the vertex set of G to the set {a | 0 ≤ a ≤ 3q-2 and either a≡0(mod 3) or a≡1(mod 3) } where q is the number of edges of G and

induces a bijection

from the edge set of G to

given by

and the function

is called one modulo three mean labeling of G. Furthermore, we prove that some standard graphs are one modulo three mean graphs.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 302-306. DOI: 10.12691/ajams-2-5-2
Pub. Date: September 04, 2014

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Pseudo R² Probablity Measures, Durbin Watson Diagnostic Statistics and Einstein Summations for Deriving Unbiased Frequentistic Inferences and Geoparameterizing Non-Zero First-Order Lag Autocorvariate Error in Regressed Multi-Drug Resistant Tuberculosis Time Series Estimators

by Benjamin G. Jacob, Daniel Mendoza, Mario Ponce, Semiha Caliskan, Ali Moradi, Eduardo Gotuzzo, Daniel A. Griffith and Robert J. Novak

Original Research

In randomized clinical trials using clustered multi-drug resistant tuberculosis (MDR-TB) data, groups of human populationare routinely assigned to treatments; whereas, observations are taken onthe individual subjects using clinically-oriented explanatory covariate coefficient estimates for identifying sites of hyperendemic transmission. Further, standard methods for data analyses of clinical MDR-TB data postulate models relating observational parameters to the response variables without accurately quantitating varying observational intra-cluster error coefficient effects. Implicit in this assumption is that the effect of these error coefficient estimates are identical. However, non-differentiation of varying and constant residual within-cluster covariate coefficient uncertainty effects in a time-series clinical MDR-TB endemic transmission model can lead to misspecified forecasted predictors of endemic transmission zones (e.g., mesoendemic). In this research we constructed multiple georeferenced autoregressive hierarchical models accompanied by non-generalized predictive residual uncertainty non-normal diagnostic tests employing multiple covariate coefficient estimates clinically-sampled in San Juan de Lurigancho Lima, Peru. Initially, a SAS-based hierarchical agglomerative polythetic clustering algorithm was employed to determine high and low MDR-TB clusters stratified by prevalence data. Univariate statistics and Poisson regression models were then generated in R and PROC NL MIXED, respectively. Durbin-Watson statistics were derived. A Bayesian probabilistic estimation matrix was then constructed employing normal priors for each of the error coefficient estimates which revealed both spatially structured (SSRE) and spatially unstructured effects (SURE). The residuals in the high MDR-TB explanatory prevalent cluster revealed two major uncertainty estimate interactions: 1) as the number of bedrooms in a house in which infected persons resided increased and the percentage of isoniazid-sensitive infected persons increased, the standardized rate of tuberculosis tended to decrease; and, (2) as the average working time and the percentage of streptomycin-sensitive persons increased, the standardized rate of MDR-TB tended to increase. In the low MDR-TB explanatory time series cluster single marital status and building material used for house construction were important predictors. Latent explanatory non-normal error probabilities in empirically regressed MDR-TB clinical-sampled covariate estimates can be robustly spatiotemporally quantitated employing a first-order autoregressive resdiualized model and a Bayesian diagnostic uncertainty estimation matrix.

American Journal of Applied Mathematics and Statistics. 2014, 2(5), 252-301. DOI: 10.12691/ajams-2-5-1
Pub. Date: August 27, 2014

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