OICC Press Mathematical Sciences 2251-7456 20 3 2026 09 30 Reliability Analysis of Log-Exponential Transformations under Progressive type-II Censoring with Medical Applications 10.57647/mathsci.2026.2003.19 EN Peyman Senobari Department of Mathematics, CT.C., Islamic Azad University, Tehran, Iran Mohsen Kokabinezhad Department of Mathematics, CT.C., Islamic Azad University, Tehran, Iran Ezzatallah Baloui Jamkhaneh Department of Statistics, QaS.C., Islamic Azad University, Qaemshahr, Iran https://orcid.org/0000-0002-4474-0225 Leila Golshani Department of Mathematics, CT.C., Islamic Azad University, Tehran, Iran Journal Article 2026 09 30 In the present paper, we propose a flexible and comprehensive family of distributions derived using the Log-Exponential transformation method within the framework of the progressive type-II censoring scheme. This new family is adaptable to various data types, as its probability density function can assume multiple forms. Beyond presenting this flexible family, we study its statistical properties and invariant estimation techniques, including the maximum likelihood and maximum product spacing estimation. We also conduct a reliabil-ity analysis of the new family, with a focus on the modified Weibull distribution as a special case. The Monte Carlo simulations are provided to assess the performance of the proposed estimation methods of the parameters and reliability function under the progressive type-II censoring. Our study emphasizes mod-eling COVID-19 data using this new family and performing reliability analysis under progressive type-II censoring, accompanied by a thorough discussion on estimation. The applicability of the proposed family is demonstrated using two COVID-19 data sets and comparisons with competitor distributions.