Cubic lower record-based transmuted family of distributions: Theory, Estimation, Applications

TL;DR

This paper introduces a new cubic lower record-based transmuted distribution family, explores its properties, compares estimation methods via simulation, and demonstrates its superior fit to real data.

Contribution

The paper proposes a novel distribution family with a special case as an alternative exponential, and evaluates estimation methods and real-world applicability.

Findings

Minimum absolute distance estimator outperforms maximum likelihood in simulations.

The proposed distribution fits real data better than competitors.

Simulation confirms the effectiveness of the estimation methods.

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.