The record-based transmuted gompertz distribution: Properties, estimation, and applications to lifetime data

• A novel Record-based Transmuted Gompertz (RTG) distribution is introduced for lifetime data modelling. • Statistical and reliability properties of the RTG distribution are thoroughly derived. • Parameter estimation is carried out using maximum likelihood with performance assessed via Monte Carlo simulation. • Real engineering datasets demonstrate the superior fitting ability of the RTG distribution over competing models. This study introduces a novel distribution model called the record-based transmuted Gompertz distribution, which extends the classical Gompertz model using a record-based transmutation approach. Several statistical properties of the proposed distribution are derived, including moments, quantile function, moment generating function, order statistics and Rényi entropy. Reliability measures such as the survival and hazard rate functions are also investigated, demonstrating flexible aging behavior suitable for reliability analysis. A stochastic comparison based on usual stochastic ordering is conducted to examine the relative reliability performance of systems modeled by the proposed distribution. Further, the parameter estimation is carried out using maximum likelihood estimation method, and the performance of the estimators is assessed through an extensive Monte Carlo simulation study. The flexibility and applicability of the introduced model are illustrated using real lifetime datasets, where it shows superior fitting performance compared to several existing Gompertz-type models, highlighting its effectiveness in modeling record-driven and extreme lifetime data. Finally, we concluded our findings by outlining the possible future scope of the present study.