Abstract
In this paper, we investigate the maximum likelihood estimates (MLEs) for the parameters of the Exponential Delay Time Distribution (EDTD) under Type-II double censoring, with extensions to right censoring, left censoring, and complete data scenarios. The limit distribution is analytically derived with some key properties in the same case. The Rényi entropy is formulated, with differential and Quadratic entropies obtained as special cases. A Monte Carlo simulation is carried out to evaluate the performance of the estimated parameters in terms of bias and mean squared error (MSE) under various censoring intensities. Approximate confidence intervals are also constructed using the Wald method. In addition, we demonstrate the practical applicability of the model through a comprehensive analysis of a real-world Waiting Time Banking dataset, showing the superiority of our model supported by goodness of fit tests. Finally, we draw our conclusions with a discussion of the results and potential for future research.