عنوان مقاله [English]
In accidents statistical modeling process, determination of the exact constant coefficients model is crucial to encounter. These coefficients express the amount and value of an independent variable with the dependent variable and for this reason incorrect estimation of them can provide inaccurate results lead to false by the model. To determine the constant coefficients models of accidents predicts an optimization process such as “squared residuals” or “maximizing log likelihood” is used. This process, generally with some optimization method called "gradient vector" and "quasi Newton" are run and in fact these methods is applied in most models predict accidents, particularly in nonlinear functions. However, these methods have some difficulties such as: long run time steps, dependence on initial value to start the process of optimization and enables us to create a convergence point in having the highest peaks are, the process optimization with problematic and made accurate calculation model coefficients are greatly diminished. In this article, using the mathematical principles is presented to minimize above mentioned problems and the appropriate facilities for modeling and optimization for models or estimated coefficients to predict accidents provides. This extrapolation method with a quadratic equation and delete words of Hessian matrix optimization method to determine the long gun gradient vector optimization result have two characters: i) in the implementation of process optimization starting moving point is not affiliated with ii) convergence for a function accidents in the forecast may create to the highest peak. The methods called "Modified gradient method vector" is on a road safety performance function tested and the superiority of the escape to the normal gradient vector method is proved.