Weighted Nonlinear Least Squares Technique for Parameters Estimation of the NHPP Gompertz Model

With the problem of heteroscedasticity an alternative precise estimation method of the nonlinear least squares (NLS) technique is needed. Weighted nonlinear least squares estimation (WNLSE) technique is an alternative that may increase the accuracy of parameters estimation by assigning suitable weights to the time between failures data. In the present study, the traditional maximum likelihood (ML), nonlinear least squares (NLS), and weighted nonlinear least squares (WNLS) techniques are formulated to estimate the three parameters of the NHPP Gompertz model. Empirical weighting method is investigated in NHPP Gompertz model prediction process. Three real software failure data examples are provided to analyze the performance of the three considered methods of estimation. The results of this numerical study indicate the preferences to the WNLSE method with respect to the NHPP Gompertz model’s performance, also the value of the weighting factors which give the optimum solution differ according to the nature of software failure data.