On UMVUE of the Parameter of OPPE and NDOPPE Family of Distributions: Accepted January 2026

This article derives closed-form uniformly minimum variance unbiased estimators (UMVUEs) for the parameters of the OPPE and NDOPPE families of distributions. Their performance is evaluated against maximum likelihood estimators (MLEs) through a simulation study with respect to bias and mean squared error (MSE). The results demonstrate that UMVUEs provide better efficiency compared to MLEs. While explicit expressions for the asymptotic variances of MLEs are obtained, the exact variances of UMVUEs appear to be analytically intractable; however, their UMVUEs are derived. To support the theoretical results, real data applications are presented where model selection and goodness-of-fit tests for OPPE and NDOPPE families are performed. For the cited datasets, both MLEs with their estimated asymptotic variances and UMVUEs with the UMVUEs of their variances are computed. The findings consistently recommend UMVUEs due to their closed-form availability and improved performance in terms of bias and MSE.