A Weibull COMP-Bessel distribution to analyse life testing data

Abstract In this paper, we deal with a problem in which the items are arranged in a series system and the sample size is unknown, giving rise to a proportional hazard model. More specifically, we propose a model where the baseline distribution is Weibull, and the distribution of the sample size is COMP-Bessel resulting in a Weibull COMP-Bessel (WCOMPB) distribution. The maximum likelihood estimators of the parameters are studied and their performance is examined by extensive simulation studies. The penalised maximum likelihood estimation procedure is used to resolve computational challenges due to the complexity of the generalization. A score test is presented to compare its performance to its sub-model. To illustrate the significance of the proposed model, three real datasets are examined and it is shown that WCOMPB fits better than several existing models.