Publication

Abstract : Probability distribution plays a vital role in lifetime data analysis, reliability modeling, and survival studies. Classical models often exhibit limitations in flexibility when dealing with diverse real-world datasets.To address this gap, we introduce an extended model that improves the ability to capture various shapes of lifetime distributions.In this paper, we propose a new three-parameter probability distribution, termed the Alpha Logarithmic Transformation of Lomax (ALTLx) distribution, which proves to be effective for modeling lifetime data.The proposed distribution is studied in detail, and several of its statistical properties are derived, including moments, incomplete moments, quantiles, mean residual life, mean inactivity time, entropy, order statistics, and stress strength analysis.Parameter estimation is carried out using the method of maximum likelihood to ensure reliable inference. The practical applicability of the ALTLx distribution is demonstrated by fitting it to datasets representing the survival time of patients. The results indicate that it outperforms several well-known competing distributions, showing that the proposed model provides a significantly better fit. The distribution exhibits greater flexibility and effectively captures diverse patterns in lifetime data. The findings confirm that the ALTLx distribution offers superior performance in modeling lifetime and reliability data.