American Journal of Applied Mathematics and Statistics

Demographic and Health Surveys (DHS) collect information on several landmark events retrospectively from the life or birth histories and recollections of past events of individuals. Retrospective information of the sort is known to be affected by recall errors which result in the misplacement of dates, and the distortion of reports of duration. For example, the retrospectively reported ages of weaning for all births that occurred during the three or five years preceding the survey are right censored and commonly display marked heaping at durations 12, 18 and 24 months. The present article at first tries to understand whether the heaping is a result of true behavior and societal norms or it is an age dependent outcome. Further, under an additive error model, a kernel-type deconvolving density estimator of weaning time is proposed by smoothing the increments of Kaplan-Meier (KM) cumulative distribution function. Using simulated data it has been shown that in small and moderately censored samples these estimators can reduce the bias substantially. Finally, an empirical illustration is provided using National Family Health Survey (NFHS-3, 2005-06) data from India.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 416-422. DOI: 10.12691/ajams-2-6-10
Pub. Date: January 06, 2015

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Comparing the Performance of Zero Mean Classification Functions under Unequal Misclassification Cost

by Michael Asamoah-Boaheng, Atinuke O. Adebanji and Nkansah Ababio

Original Research

In this study the performance of Minimum Expected Cost of Misclassification method (MECM) and Quadratic Discriminant Function approach (QDF) were compared and evaluated for the case of equal mean discrimination under unequal misclassification cost. 30 pairs of Female liked sex twins extracted from Stocks (1933) ten (10) variate data on 832 twin children was used for evaluation. Discriminant functions were derived under each of the following misclassification cost ratios; 1: 1, 1: 2, 1: 3 and 1: 4 and their error rate estimates determined using the Cross Validation (CV) and Balanced Error Rate (BER) methods. Least Mean error rates were recorded under QDF method as compared to that of MECM. The error rate estimates showed the QDF outperforming the MECM in the provision of maximum separation between the two groups. Also the two classification rules were found to be sensitive to misclassification cost ratios exceeding 1:2.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 409-415. DOI: 10.12691/ajams-2-6-9
Pub. Date: December 26, 2014

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Trend and Levels of Women Empowerment in Nigeria

by ACHA and CHIGOZIE KELECHI

Meta-Analysis

Women empowerment has become major factor in economic development and is increasingly at the core of countries’ competitiveness in the global economy. The main objective of this paper is to ascertain the trend and level of women empowerment in Nigeria by 2015. Secondary data from Nigeria Demographic and Health Survey (NDHS), Nigeria Demographic and Education Survey (NDES), and National Population Commission (NPC) were used. Employment, education and literacy rate were adopted as measures of women empowerment. An overview of the relationship between women’s level of education and other background characteristics was carried out. The results showed that men are more likely than women to have some education. Over 40 percent of men are literate compared to 13 percent of women, which is similar to the results obtained from variables like occupation, agriculture, etc. Employment is one source of empowerment for women but unfortunately it is difficult to measure their employment status because the informal sectors are not reported. However, the data on hand indicates, for instance, that women and men currently employed in the North West are 46 and 54 percent respectively. Also, the employment rate of men and women in urban area are of the ratio 42:37 percent while the employment ratio of men to women in the rural area is 63:58. The study also hints that employment, education and literacy rate of women are strong determinants of economic growth and they should not be neglected as the nation works toward attaining vision 2020 goals.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 402-408. DOI: 10.12691/ajams-2-6-8
Pub. Date: December 22, 2014

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The Fourier, Laplace Transformations and the Newton Potential

by Andrey Pavlov V.

Original Research

With help of a methods of Fourier`s analysis we consider the analytic continuation of Laplace transformation (with help a values on the complex axis) to the left part of plane, when the continuation is odd ore even.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 398-401. DOI: 10.12691/ajams-2-6-7
Pub. Date: December 14, 2014

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On Proper Classification and Placement of Students in Nigerian University Systems Using Discriminant Analysis

by G. O. Nwafor and C. E Onwukwe

Case Study

This paper attempts to provide more realistic and reliable way of placing Nigerian students seeking admission into Nigerian University system using Discriminant Analysis and also providing quantitative analysis of a Discriminant Analysis approach to prediction of student’s admission scores into a university system. The paper utilizes secondary data sourced from the Admission and Public Relation Department of Cross Rivers University of Technology Calabar, the conditions for predictive and classification discriminant analysis were obtained, and the empirical result yield a discriminant linear classification function results on the various faculties of interest on the method of admission system obtainable in Nigeria university system. The study reveals university mandatory examination (UME) and Aptitude Test score of students in their various faculties. The linear function established a hit ratio of 83% of which successfully predicted the student admission scores. The study had apparent error rate of 17% which explains the probabilities of misclassification.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 394-397. DOI: 10.12691/ajams-2-6-6
Pub. Date: December 03, 2014

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Some Restricted Partition Functions

by Sabuj Das

Original Research

In 1742, Euler found the generating function for P(n). Hardy said Ramanujan was the first, and upto now the only, Mathematician to discover any such properties of P(n). In 1952, Macmahon established a table of P(n) for the first 200 values of n. This paper showed how to find the number of partition of n by using Macmahon’s table. In 1742, Euler also stated the series in the enumeration of partitions. This Paper showed how to generate the Euler’s use of series in the enumeration of partitions. In 1952, Macmahon also quoted the self-conjuate partitions of n. In this Paper, Macmahon’s self-conjugate partitions are explained with the help of array of dots. This paper showed how to prove the Euler’s Theorems with the help of Euler’s device of the introduction of a second parameter z, and showed how to prove the Theorem 3 with the help of Euler’s generating function for P(n), and also showed how to prove the Theorem 4 with the help of certain conditions of P(n).

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 386-393. DOI: 10.12691/ajams-2-6-5
Pub. Date: December 01, 2014

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A Multivariate Time Series Modeling of Major Economic Indicators in Nigeria

by C. E Onwukwe and G. O. Nwafor

Original Research

One of the key objectives of every good economy, whether or not developing or developed is to achieve a high and sustainable economic growth rate coupled with the economic indicators. The research on the Multivariate Time Series Modeling of Major Economic Indicators in Nigeria, aims at providing quantitative analysis of the dynamics on currency in circulation, exchange rate, external reserve, gross domestic product, money supply and price deflator. This study utilizes secondary data obtained from the Central Bank of Nigeria, Statistical Bulletin (vol. 21: 2010), of all variables investigated in the model. The sample covers quarterly data from 1981 to 2010. The study employed the newly developed multivariate time series estimation technique via Vector Autoregressive modeling to model the economic indicators in Nigeria. The empirical result yields a stable and sustainable economic model for the six economic variables in the study. The Granger causality analysis indicates that there exists unidirectional and bidirectional causality between the economic variables. Gross domestic product and external reserve was seen as a good predictor to other economic indicators. The relationship between these economic indicators is however significantly determined which is positive in either direction. The empirical model provides forecast value for the next two years.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 376-385. DOI: 10.12691/ajams-2-6-4
Pub. Date: November 30, 2014

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The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

by Gandel Yu. V. and Dushkin V.D.

Original Research

In this article the method for numerical solution of boundary integral equations of the original problem is proposed. This method is one of the modifications of Nystrom-type methods; particularly the method of discrete vortices. The convergence of the numerical solutions to the exact solution of the problem is guaranteed by propositions proved in this article. Also, the rate of convergence of the approximate solutions to the exact solution had been found.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 369-375. DOI: 10.12691/ajams-2-6-3
Pub. Date: November 26, 2014

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The Exponentiated Lomax Distribution: Different Estimation Methods

by Hamdy M. Salem

Original Research

This paper concerns with the estimation of parameters for the Exponentiated Lomax Distribution ELD. Different estimation methods such as maximum likelihood, quasi-likelihood, Bayesian and quasi-Bayesian are used to evaluate parameters. Numerical study is discussed to illustrate the optimal procedure using MATHCAD program (2001). A comparison between the four estimation methods will be performed.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 364-368. DOI: 10.12691/ajams-2-6-2
Pub. Date: November 18, 2014

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Application of Binary Logistic Regression in Assessing Risk Factors Affecting the Prevalence of Toxoplasmosis

by Mutangi Kudakwashe and Kasim Mohammed Yesuf

Original Research

Toxoplasmosis is a parasitic disease caused by the protozoan parasite Toxoplasma Gondii (T.gondii). The parasite infects warm-blooded animals among them humans especially those whose immunity has been compromised. The transmission mode of the parasite vary from living in unhygienic conditions, contact with cat faeces to contact with raw meat or the practice of raw meat eating, such as commonly practiced in Ethiopia. Binary logistic regression was used to determine the risk factors affecting the prevalence of toxoplasmosis in HIV/AIDS patients. Significant risk factors were detected using the Wald and the likelihood ratio tests. The model selected was then subjected to diagnostic checks to assess its fitness using the Hosmer and Lemeshow test as well as the Pearson, and deviance goodness of fit tests. The results showed that patients living under unhygienic conditions, aged patients, illiterate and less educated patients were mostly affected by toxoplasmosis. There was more prevalence in urban areas than in rural areas possibly due to the high density of people in urban areas.

American Journal of Applied Mathematics and Statistics. 2014, 2(6), 357-363. DOI: 10.12691/ajams-2-6-1
Pub. Date: November 18, 2014

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