by Dharmaratne ADVTT and Sooriyarachchi MR
Original Research
Binary repeated measurements occur often in a variety of fields. Particularly in medicine, small samples are used in the early phases (phase I and II) of clinical trials, in bio equivalence studies and in crossover trials where human participation is multitudinous. Hence, it is vital to develop a precise method to analyze binary Repeated Measures Data (RMD) with small sample size which is related to humans and even to animals. As a result, this simulation study was carried out in SAS to examine the performance of the two methods used with general sample sizes; the Generalized Estimating Equations (GEE) method and Generalized Linear Mixed Models (GLMM) towards analysis of binary RMD with small sample size, after adjusting the bias that occurs in small samples. Being motivated by the study of literature, large scale simulations are carried out for each method with the facilitation of PROC GENMOD and PROC GLIMMIX procedures respectively, along with varying options of small sample bias correction methods available in SAS, the Sandwich Variance Estimation (SVE) technique and its variants. Each method with all possible SVE techniques available in SAS were compared and contrasted with respect to the properties; Type I error, power, unbiasedness, consistency, sufficiency, convergence, speed of computation and efficiency. The results obtained from the simulation study depicted that for binary RMD which adhere to AR(1) process, with no missing values and with no covariates, GLMM with SVE techniques FIROEEQ and ROOT perform equally and exceptionally well for a small sample size binary repeated case with respect to all the properties of parameter estimates considered except for sufficiency. However the GEE method with the naive option while being marginal with respect to type I error, performs well in analyzing very small sample sizes and satisfies all the properties including sufficiency.
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 80-89. DOI: 10.12691/ajams-5-2-6
Pub. Date: July 29, 2017
10440 Views2116 Downloads
by Mohammad Alryalat, Richmond Adebiaye and Haroun Alryalat
Original Research
Information technology (IT) investment and aligning methodologies require thorough understanding of analyses on different parallel present values and strong internal rates of return. E-commerce has given a new dimension to IT investing that elevates the role of strong IT performance as a driver of corporate strategy. Stakeholders concerned with maximizing IT return on investment (ROI) recognize the importance of central, comprehensive information resources to effective strategic business planning. Alignment of corporate and IT strategies is now a vital element of business success. To empirically support this conclusion, this study measures the relationship between strategic alignment of IT investment returns and corporate performance. A Descriptive research design using survey methodology was employed. The study included analyses of variable values involving stakeholders in banks, such as new customers and employees. A Simple Percentage Method, chi-square tests, Tables and weighted average were used to analyze data of at least five (5) banks in Ajman Emirates of UAE to determine the degree of alignment and its impact on the two strategic dimensions. A binary logistic regression analysis using Chan¡¯s STROIS model incorporated with Venkatraman¡¯s STROBE model was proposed to collect survey data and determine the extent of the strategic alignment. The research results provide empirical evidence that supports the hypothesis that closer alignment between corporate and IT strategies leads to increased IT ROI and improved corporate performance. This relationship holds true for all firms regardless of strategic intent for IT. The study also shows a positive correlation between early adoption of newly emergent technologies and business competitive advantage which leads to positive conclusions that strategic competition is imperative towards corporate performances.
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 72-79. DOI: 10.12691/ajams-5-2-5
Pub. Date: July 21, 2017
15641 Views2925 Downloads1 Likes
by Bright O. Osu, Samson O. Eggege and Emmanuel J. Ekpeyong
Original Research
In this work, the Generalized Binomial Distribution (GBD) combined with some basic financial concepts is applied to generate a model for determining the prices of a European call and put options. To demonstrate the behavior of the option prices (call and put) with respect to variables, some numerical examples and graphical illustration have been given in a concrete setting to illustrate the application of the obtained result of the study. It was observed that when there is an increase in strike prices, it leads to decrease in calls option priceC(0) and increase in puts option price P(0). Decrease in interest rate leads to decrease in calls option priceP(0), and increase in puts option price P(0), and decrease in expiration date leads to decrease in calls option price C(0) and decrease in puts option price P(0). It was also found that the problem of option price can be approached using Generalized Binomial Distribution (GBD) associated with finance terms.
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 62-71. DOI: 10.12691/ajams-5-2-4
Pub. Date: July 20, 2017
12994 Views2572 Downloads8 Likes
by Opara Jude, Oruh Ben Ifeanyichukwu, Iheagwara Andrew Ihuoma and Esemokumo Perewarebo Akpos
Original Research
In this research, a new and efficient approach of finding an initial basic feasible solution to transportation problems is proposed. The proposed approach is named “Inverse Coefficient of Variation Method (ICVM)”, and the method is illustrated with seven numerical examples. Six existing methods; North West Corner Method (NWCM), Column Minimum Method (CMM), Least Cost Method (LCM), Row Minimum Method (RMM),Vogel’s Approximation Method (VAM), and Allocation Table Method (ATM) were compared with the proposed approach. It can be said conclusively that the proposed Inverse Coefficient of Variation Method (ICVM) provides an improved Initial Basic Feasible Solution to all the transportation problems used in the experiment. Further, the new method leads to the optimal solution to many of the problems considered.
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 54-61. DOI: 10.12691/ajams-5-2-3
Pub. Date: July 06, 2017
13643 Views2124 Downloads
by Matthew Chukwuma Michael, Oyeka Cyprain Anene, Ashinze Mpuruoma Akudo and Igabari John Nwabueze
Original Research
This paper seeks to develop a generalized method of generating the moments of random variables and their probability distributions. The Generalized Moment Generating Function is developed from the existing theory of moment generating function as the expected value of powers of the exponential constant. The methods were illustrated with the Beta and Gamma Family of Distributions and the Normal Distribution. The methods were found to be able to generate moments of powers of random variables enabling the generation of moments of not only integer powers but also real positive and negative powers. Unlike the traditional moment generating function, the generalized moment generating function has the ability to generate central moments and always exists for all continuous distribution but has not been developed for any discrete distribution.
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 49-53. DOI: 10.12691/ajams-5-2-2
Pub. Date: July 05, 2017
9588 Views2931 Downloads
by Ahmed Elshahhat
Review Article
Based on Type-I and Type-II generalized progressive hybrid censoring schemes, the maximum likelihood estimators and Bayes estimators for the unknown parameters of exponentiated Weibull lifetime model are derived. The approximate asymptotic variance-covariance matrix and approximate confidence intervals based on the asymptotic normality of the classical estimators are obtained. Independent non-informative types of priors are considered for the unknown parameters to develop the Bayes estimators and corresponding Bayes risks under a squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. Finally, one real data set is analyzed for illustrative purposes.
American Journal of Applied Mathematics and Statistics. 2017, 5(2), 33-48. DOI: 10.12691/ajams-5-2-1
Pub. Date: April 11, 2017
16514 Views3117 Downloads1 Likes