A Novel Unit Exponential Delay Time Distribution: Theory, Inference and Applications

This paper introduces the Unit Exponential Delay Time Distribution (UEDTD), a two-parameter model for data with support in the unit interval (0,1). The model is derived using two distinct approaches: transformation method applied to the Exponential Delay Time Distribution (EDTD), which itself arises as the convolution of two independent exponential random variables, and product convolution method of two independent power-function random variables that connects UEDTD to Pareto distribution, offering additional interpretability and giving rise to several exact and efficient algorithms for generating random samples. The limit distribution is examined with derivation of key statistical properties. The order statistics with interesting asymptotic results for extremes distribution are discussed and formulated. A reparameterization for the model is suggested to improve estimation stability and formulation with maximum likelihood approach employed for parameter inference. A simulation study demonstrates the consistency and efficiency of the estimators across various sample sizes and parameter configurations. The practical applicability of the UEDTD is demonstrated through a real-world dataset, where it shows superior performance compared to established unit distributions, confirming the utility of the UEDTD for modeling proportional data in applied research.