Accuracy of the Jian-Yang-Jiang-Liu-Liu Spectral Conjugate Gradient Method in Estimating Extended Exponential Weibull Parameters

Abstract

Life is filled with uncertainty and risk. The analysis of lifetime is needed to be a tool that can manage uncertainty. Lifetime is defined as data that contains the time until the occurrence of an event. Based on its definition, lifetime data is like Hazard rate data or mortality data because mortality data can be defined as data that contains the probability of an object surviving until that moment per unit time interval. The analysis of mortality data aims to model the distribution of time to event and/or the determinants of time to event. One of the distribution models that can be used to analyze mortality data is Weibull distribution. However, the Weibull distribution is not very suitable for modeling the more complex versions of data. Therefore, an extension of the Weibull distribution that is more flexible in modeling data is used, namely the Extended Exponential Weibull (ExEW) distribution. The ExEW distribution has four parameters whose estimation can be calculated using the maximum likelihood estimation (MLE) method. However, parameters estimated with MLE are often too difficult to calculate analytically, hence the use of optimization methods. One of the optimization methods that can be used to determine the estimated parameters of the ExEW distribution is the conjugate gradient method. To date, many conjugate gradient methods have been developed, including the Liu-Feng-Zou (LFZ) spectral conjugate gradient method and the Jian-Yang-Jiang-Liu-Liu (JYJLL) spectral conjugate gradient method. Previous research suggests that the JYJLL spectral conjugate gradient method has more efficient computational performance than the LFZ spectral conjugate gradient method. Through data simulation, this study provides results that the JYJLL spectral conjugate gradient conjugate method has better accuracy than the LFZ spectral conjugate gradient method in parameter estimation of the ExEW distribution. In addition, the ExEW distribution is the most suitable distribution in modeling various forms of Hazard rate data compared to the Weibull and exponential distributions.