Open Access Original Research Article

Modeling Count Data from Dependent Clusters with Poisson Mixed Models

K. A. N. K. Karunarathna, Pushpakanthie Wijekoon

Asian Journal of Probability and Statistics, Page 1-21
DOI: 10.9734/ajpas/2018/v1i224505

Responses collected from dependent clusters are affected by the dependence among clusters and it should be taken into account in modeling such responses. In this study, a new approach was evaluated to incorporate cluster dependence in generalized linear Poisson mixed models for count responses from dependent clusters. Performance of this approach was evaluated by using a simulation process under three different designs and different covariates. The Marginal Generalized Quasi-likelihood (GQL) method was used for estimation of parameters with the cluster dependence. Monte Carlo likelihood (MCL) and Penalized Quasi-likelihood (PQL) estimates also were obtained for the purpose of comparison.  Proposed approach was tested with a real data set also.

The proposed approach, with the incorporation of cluster dependence, gives better estimates for both fixed effects and variance of random effects with low standard errors with compared to the estimates obtained by ignoring the cluster dependence. Therefore, the proposed approach can be used for modeling count responses from a dependent cluster set up.

Open Access Original Research Article

A Mathematical Model that Analyzes the Differences between the Cost of Maintaining the Desired Permanent Workforce (Academic Staff) and that of Maintaining the Entire Outsourcing Policy for Private Universities in Nigeria

O. Enagbonma, A. A. Osagiede

Asian Journal of Probability and Statistics, Page 1-11
DOI: 10.9734/ajpas/2018/v1i224510

The difference between the cost of maintaining the desired permanent workforce (academic staff) and that of maintaining the entire outsourcing policy is a useful index that allows management of private universities to know the financial task before them, well ahead of time for a possible solution. However, in the available literature, there are no adequate mathematical models that address such issues. The idea of linear algebra was used to develop a mathematical model that can address such real-life problem.

 

Open Access Original Research Article

Efficiency of Bayesian Approaches in Quantile Regression with Small Sample Size

Neveen Sayed-Ahmed

Asian Journal of Probability and Statistics, Page 1-13
DOI: 10.9734/ajpas/2018/v1i224527

Quantile regression is a statistical technique intended to estimate, and conduct inference about the conditional quantile functions. Just as the classical linear regression methods estimate model for the conditional mean function, quantile regression offers a mechanism for estimating models for the conditional median function, and the full range of other conditional quantile functions. In the Bayesian approach to variable selection prior distributions representing the subjective beliefs about the parameters are assigned to the regression coefficients. The estimation of parameters and the selection of the best subset of variables is accomplished by using adaptive lasso quantile regression. In this paper we describe, compare, and apply the two suggested Bayesian approaches. The two suggested Bayesian suggested approaches are used to select the best subset of variables and estimate the parameters of the quantile regression equation when small sample sizes are used.  Simulations show that the proposed approaches are very competitive in terms of variable selection, estimation accuracy and efficient when small sample sizes are used. 

 

Open Access Original Research Article

Group Divisible Variance – Sum Third Order Rotatable Design through Balanced Incomplete Block Designs in Four Dimensions

N. Chebet, M. Kosgei, G. Kerich

Asian Journal of Probability and Statistics, Page 1-9
DOI: 10.9734/ajpas/2018/v1i224529

In the study of rotatable designs, the variance of the estimated response at a point is a function of the distance of that point from a particular origin. Group divisible Rotatable Designs have been evolved by imposing conditions on the levels of factors in a rotatable design. In Group Divisible Third Order Rotatable Designs (GDTORD), the v-factors are split into two groups of p and (v-p) factors such that the variance of a response estimated at a point equidistant from the centre of the designs is a function of the distances  and from a suitable origin for each group respectively. Where  and   denotes the distances of the projection of the points in each of the group from a suitable origin respectively. In this paper, a four dimensional Group Divisible Variance-Sum Third Order Rotatable Design is constructed using a balanced incomplete block design.

 

Open Access Review Article

Comparison of Goodness of Fit Tests for Normal Distribution

I. Agu, Friday, E. Francis, Runyi

Asian Journal of Probability and Statistics, Page 1-32
DOI: 10.9734/ajpas/2018/v1i224507

Goodness of fit test is a test that has attracted researchers’ interest over the decades. This study is on goodness of fit test for normal distribution only. The Kolmogorov-Smirnov (K-St) and Pearson’s Chi-square (χ² test) goodness of fit test were used to determine the normality of a given data.  The result revealed that the data is normal under the two tests and that the Kolmogorov-Smirnov (K-S test) were preferred to Pearson’s Chi-square (χ² test). The Kolmogorov-Smirnov (K-S) test of goodness of fit is the most suitable in terms of the p-value.