Exploring the Beta Linear Failure Rate Geometric Distribution: Properties and Applications

Abstract

This paper introduces the Beta Linear Failure Rate Geometric (BLFRG) distribution, a flexible model that encompasses various well-known distributions as special cases, including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh, and exponential distributions. The BLFRG distribution generalizes the linear failure rate distribution and provides a broader framework for modeling lifetime data. The paper thoroughly investigates the model's properties, including its moments, conditional moments, deviations, Lorenz and Bonferroni curves, and entropy, offering a comprehensive understanding of its behavior. The paper also discusses the estimation methods for the model parameters. To demonstrate its practical utility, the BLFRG distribution is applied to real data examples, showcasing its effectiveness in capturing various patterns in lifetime data. The BLFRG distribution provides a versatile tool for reliability analysis and can be utilized in various applications involving lifetime data with different failure patterns.