This paper develops a multiplicative model, termed the multiplicative Burr III distribution, by analyzing a parallel system consisting of two independently operating components, each having a Burr III-distributed lifetime. The multiplicative Burr III distribution is appropriate for modeling positively, negatively skewed, leptokurtic, platykurtic and over- and under-variation real data. A graphical illustration of the proposed model’s probability density, hazard rate, and reversed hazard rate functions is presented. The plots of the pdf and hrf of the multiplicative Burr III distribution exhibit approximately symmetric or unimodal shapes depending on the parameter values. This flexibility highlights the model’s capability to represent both symmetric and asymmetric behaviors in lifetime data. The fundamental characteristics of the multiplicative Burr III distribution are thoroughly established. Parameter estimation, along with the reliability, hazard rate, and reversed hazard rate functions, is conducted using the maximum likelihood approach. In addition, asymptotic confidence intervals are derived for the parameters and associated reliability and hazard functions. A comprehensive simulation study is performed to assess the efficiency of the maximum likelihood estimators. Finally, the practical relevance of the proposed distribution is validated through real-life datasets.
Salem et al. (Mon,) studied this question.