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### Article

A Shared Parameter Model for Longitudinal Data with Missing Values

1Department of Statistics, Faculty of Economics and Political Science, Cairo University, Cairo, Egypt

American Journal of Applied Mathematics and Statistics. 2013, 1(2), 30-35
DOI: 10.12691/ajams-1-2-3

Cite this paper:
Ahmed M. Gad, Nesma M. M. Darwish. A Shared Parameter Model for Longitudinal Data with Missing Values. American Journal of Applied Mathematics and Statistics. 2013; 1(2):30-35. doi: 10.12691/ajams-1-2-3.

Correspondence to: Ahmed M. Gad, Department of Statistics, Faculty of Economics and Political Science, Cairo University, Cairo, Egypt. Email: ahmed.gad@feps.edu.eg

### Abstract

Longitudinal studies represent one of the principal research strategies employed in medical and social research. These studies are the most appropriate for studying individual change over time. The prematurely withdrawal of some subjects from the study (dropout) is termed nonrandom when the probability of missingness depends on the missing value. Nonrandom dropout is common phenomenon associated with longitudinal data and it complicates statistical inference. The shared parameter model is used to fit longitudinal data in the presence of nonrandom dropout. The stochastic EM algorithm is developed to obtain the model parameter estimates. Also, parameter estimates of the dropout model have been obtained. Standard errors of estimates have been calculated using the developed Monte Carlo method. The proposed approach performance is evaluated through a simulation study. Also, the proposed approach is applied to a real data set.

### References

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### Article

Generalised Common Fixed Point Theorems of A-Compatible and S-Compatible Mappings

1National Institute of Technology Manipur, Imphal, India

American Journal of Applied Mathematics and Statistics. 2013, 1(2), 27-29
DOI: 10.12691/ajams-1-2-2

Cite this paper:
Shahidur Rahman, Yumnam Rohen, M. Popeshwar Singh. Generalised Common Fixed Point Theorems of A-Compatible and S-Compatible Mappings. American Journal of Applied Mathematics and Statistics. 2013; 1(2):27-29. doi: 10.12691/ajams-1-2-2.

Correspondence to: Yumnam Rohen, National Institute of Technology Manipur, Imphal, India. Email: ymnehor2008@yahoo.com

### Abstract

In this paper we prove a common fixed point theorem of four self mappings satisfying a generalized inequality using the concept of A-compatible and S-compatible mappings. Our result generalizes many earlier related results in the literature.

### References

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### Article

Pursuit and Evasion Game under Uncertainty

1Department of Actuarial Science and Insurance Faculty of Business Administration University of Lagos Akoka, Lagos

American Journal of Applied Mathematics and Statistics. 2013, 1(2), 21-26
DOI: 10.12691/ajams-1-2-1

Cite this paper:
Bankole Abiola, R.K. Ojikutu. Pursuit and Evasion Game under Uncertainty. American Journal of Applied Mathematics and Statistics. 2013; 1(2):21-26. doi: 10.12691/ajams-1-2-1.

Correspondence to: R.K. Ojikutu, Department of Actuarial Science and Insurance Faculty of Business Administration University of Lagos Akoka, Lagos. Email: rkojikutu@Unilag.edu.ng

### Abstract

This paper examined a class of multidimensional differential games. In particular, it considered a situation in which the pursuer and evader are affected by uncertain disturbances. A necessary and sufficient condition for the existence of saddle point for this class of games was developed.

### References

 [1] Abiola, B.(2012) “On Generalized Saddle Point Solution for a Class of Differential Games” International Journal of Science and Advanced Technology, 2(8):27-31. [2] Abiola, B.(2009) “Control of Dynamical Systems in The Presence of Bounded Uncertainties” Unpublished PhD Thesis , Department of Mathematics University of Agriculture Abeokuta. [3] Arika, I. (1976). “Linear Quadratic Differential Games in Hilbert Space” SIAM Journal of Control and Optimization, 1(1). [4] Gutman,S, (1975). “Differential Games and Asymptotic Behaviour of Linear Dynamical Systems in the Presence of Bounded Uncertainty” PhD Dissertation, University of California, Berkley. [5] Leitmann, G, (2004) “A Direct Optimization Method and its Application to a Class of Differential Games” Journal of Dynamics of Continuous and Intensive Systems, 11, 191-204.