Asian Journal of Probability and Statistics

In reliability and survival analysis, for modeling real-life datasets bounded within a finite interval, several probability distributions characterized by location parameters are available. Among these, the uniform distribution is commonly used due to its assumption of equal probability across the specified range. The log uniform distribution is used in scenarios where varying probabilities are to be assigned across the specified range. However, in scenarios involving length-biased sampling—where larger values receive proportionally greater probabilities—the log uniform distribution becomes inadequate. To address this limitation, the present paper introduces a length-biased (weighted) log uniform distribution. The proposed weighted Log-Uniform (WLU) distribution provides greater flexibility and thereby broadens the scope of potential applications. Its statistical properties, such as moments, coefficient of variance etc. are derived, and parameter estimation is carried out using the method of maximum likelihood. The WLU distribution is significant in reliability engineering, as it belongs to increasing failure rate (IFR) family. A comprehensive simulation study is also conducted to evaluate the performance of the estimators for all the three parameters.The estimators are found to perform better with increasing sample size.