Cubic Lower Record-based Transmuted Family of Distributions: Theory, Estimation, Applications

Accepted April 2026

Abstract

In this study, a family of distributions called cubic lower record-based transmuted is provided. A special case of this family is proposed as an alternative exponential distribution. Several statistical properties are explored. We utilize nine different methods to estimate the parameters of the suggested distribution. In order to compare the performances of these methods, we consider a comprehensive Monte-Carlo simulation study. As a result of simulation study, we conclude that minimum absolute distance estimator is a valuable alternative to maximum likelihood estimator. Then, we carried out two real-world data examples to evaluate the fits of introduced distribution as well as its potential competitor ones. The findings of real-world data analysis show that the best-fitting distribution for both datasets is our model.