The Area-Biased Burhan Distribution: Structural Properties, Parametric Inference and Application to Medical Data

Abstract

Statistical modeling of survival and lifetime phenomena across clinical research, epidemiology, and healthcare analytics frequently encounters complex data structures influenced by ascertainment bias and non-random sampling. In medical applications such as analyzing patient survival times, disease recurrence, or treatment response rates, the weighted distributions offer a mathematically robust mechanism to adjust baseline probability density functions, introducing additional parametric flexibility to capture non-monotonic hazard rates and asymmetric tail behavior. Motivated by these advantages, this study proposes the area-biased Burhan distribution by applying the weighting technique to the classical Burhan distribution. We present a comprehensive theoretical investigation of the proposed model, establishing its basic probability functions, reliability measures, and key statistical properties, including moments, order statistics, and entropy measures. Unknown parameters are estimated using the method of maximum likelihood, and their finite-sample performance is validated through a Monte Carlo simulation study. Finally, the practical utility, empirical adaptability, and superior fitting performance of the area-biased Burhan distribution are demonstrated using real-world lifetime data, highlighting its efficacy as a flexible alternative to traditional lifetime distributions in medical and allied sciences.