ESTIMATION OF PARAMETERS OF A WEIBULL-TYPE NONLINEAR REGRESSION MODEL

In a nonlinear regression model parameters occur nonlinearly and, as such, the normal equations obtained by equating partial derivatives of sum of squares of error with respect to parameters do not produce least squares estimates in close form. Therefore, iterative procedures are used for the purpose. Nowadays, researchers directly minimize sum of squares of errors for a choice of parameters using nonlinear optimization algorithms. But these algorithms need good initial estimates to start iterations. If many parameters are involved, the problems of convergence may arise if initial estimates are not good enough. We may have convergence to a local minimum, slow or no convergence. In this paper, we have developed a procedure based on numerical integration for obtaining estimates of a four parameter Weibull-type nonlinear regression model and have demonstrated its application to a published data set.