Length-Biased Burhan Distribution: Properties, Simulation, and Applications

This paper introduces a novel probability distribution, the length-biased Burhan distribution, characterized by three parameters. The study involves a comprehensive analysis of the distribution, including the derivation of its probability density function, cumulative distribution function, reliability analysis, moments, moment generating function, characteristics function, ordered statistics, entropies, and Bonferroni and Lorenz curves. The maximum likelihood estimation is employed to estimate distribution parameters. The likelihood ratio test is presented for comparing the goodness of fit of the developed probability distribution over Burhan distribution. Additionally, simulation study is used to evaluate how well and reliably maximum likelihood estimators work. Finally, length-biased Burhan distribution is applied to a real-life data set, the distribution emerged as a notably better fit than other established well-known distributions.