In this paper, the error distribution function is estimated for the single index model by the empirical distribution function and the kernel distribution function. Refined minimum average variance estimation (RMAVE) method is used for estimating single index model. We use simulation experiments to compare the two estimation methods for error distribution function with different sample sizes, the results show that the kernel distribution function is better than the empirical distribution function.

Generalized Additive Model has been considered as a multivariate smoother that appeared recently in Nonparametric Regression Analysis. Thus, this research is devoted to study the mixed situation, i.e. for the phenomena that changes its behaviour from linear (with known functional form) represented in parametric part, to nonlinear (with unknown functional form: here, smoothing spline) represented in nonparametric part of the model. Furthermore, we propose robust semiparametric GAM estimator, which compared with two other existed techniques.

In this paper, a four species mathematical models involving different types of ecological interactions is proposed and analyzed. Holling type – II functional response is a doubted to describes the behavior of predation. The existence, uniqueness and boundedness of the solution are discussed. The existences and the stability analysis of all possible equilibrium points are studied. suitable Lyapunov functions are used to study the global dynamics of the system. Numerical simulations are also carried out to investigate the influence of certain parameters on the dynamical behavior of the model, to support the analytical results of the model.

      The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin

Abstract

The population is sets of vocabulary common in character or characters and it’s study subject or research . statistically , this sets is called study population (or abridgement population ) such as set of person or trees of special kind of fruits or animals or product  any country for any commodity through infinite temporal period term ... etc.

The population maybe finite if we can enclose the number of its members such as the students of finite school grade . and maybe infinite if we can not enclose the number of it is members such as stars or aquatic creatures in the sea . when we study any character for population the statistical data is concentrate by two metho

     The work in this paper focuses on solving numerically and analytically a  nonlinear social epidemic model that represents an initial value problem  of ordinary differential equations. A recent moking habit model from Spain is applied and studied here. The accuracy and convergence of the numerical and approximation results are investigated for various methods; for example, Adomian decomposition, variation iteration, Finite difference and Runge-Kutta. The discussion of the present results has been tabulated and graphed. Finally, the comparison between the analytic and numerical solutions from the period 2006-2009 has been obtained by absolute and difference measure error.

  Computer analysis of simple eye model is performed in the present work by using the Zemax optical design software 2000E . The most important optical parameters of the eye were calculated such as the effective focal length (EFL) , the image spot size at the retina and found to be in a reasonable agreement with the values needed for the laser retinal treatment .The present eye model leads to an effective wavelength and we found the image spot diagram at the surface of the retina and the wavefront error which are provided at zero field angle. This gives a good evidence of the validity of the model in one hand, and can be used to determine the compatibility of any optical design intended for visual applications. By using the pulse fre

This study aims to numerically simulate the flow of the salt wedge by using computational fluid dynamics, CFD. The accuracy of the numerical simulation model was assessed against published laboratory data. Twelve CFD model runs were conducted under the same laboratory conditions. The results showed that the propagation of the salt wedge is inversely proportional to the applied freshwater discharge and the bed slope of the flume.  The maximum propagation is obtained at the lowest discharge value and the minimum slope of the flume. The comparison between the published laboratory results and numerical simulation shows a good agreement. The range of the relative error varies between 0 and 16% with an average of 2% and a roo

In this paper, chaotic and periodic dynamics in a hybrid food chain system with Holling type IV and Lotka-Volterra responses are discussed. The system is observed to be dissipative. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov direct method. Chaos phenomena is characterized by attractors and bifurcation diagram. The effect of the controlling parameter of the model is investigated theoretically and numerically.