Record-based Transmuted Log-logistic Distribution: Properties, Simulation, and Applications to Petroleum Rock and Reactor Pump Data

Accepted November 2025

Abstract

This study aims to introduce a new lifetime distribution, called the record-based transformed log logistic distribution, to the literature. We obtain this distribution using a record-based transformation map based on the distributions of upper record values. We explore some mathematical properties of the suggested distribution, namely the quantile function, hazard function, moments, order statistics, and stochastic ordering. We discuss the point estimation via seven different methods such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, Cramer-von Mises, maximum product spacings, and right tail Anderson Darling. Then, we perform a Monte Carlo simulation study to evaluate the performances of these estimators. Also, we present two practical data examples, reactor pump failure and petroleum rock data to compare the fits of the proposed distribution with its rivals. As a result of data analysis, we conclude that the best-fitted distribution is the record-based transmuted log-logistic distribution for reactor pump failure and petroleum rock data sets.