On the Odd Burr III-Type II Generalized Exponential-G Family of Distributions: Properties with Applications to Failure Data

Abstract

This study introduces the odd Burr III-Type II Generalized ExponentialG (OBIII-TIIGE-G) family of distributions, a flexible statistical framework designed to model diverse data geometries. By synthesizing the
structural strengths of the odd Burr III-G and the type II general
exponential-G families, the proposed model addresses critical gaps in
existing distributions, particularly their inability to simultaneously capture monotonic and non-monotonic hazard rates. The OBIII-TIIGEG family offers analytical tractability, with closed-form expressions for
quantile functions, moments, and hazard rate dynamics, enabling robust reliability assessments. Monte Carlo simulations validate the consistency and efficiency of maximum likelihood estimators, showing reduced bias and root mean square error as sample sizes increase. Applied
to real-world failure datasets—carbon fiber breaking stress and silicon
nitride fracture toughness, the model demonstrates superior goodnessof-fit over six competing distributions, evidenced by lower goodnessof-fit statistics with higher p-values. Its ability to adapt to symmetric,skewed, and heavy-tailed data, coupled with identifiable parameters and
precise estimation, positions it as a vital tool for reliability engineering
and materials science. This research advances distribution theory and
provides practitioners with a versatile solution for modeling complex
failure-time phenomena.