This paper proposes the 4-parameter odd Lomax generalized exponential distribution for the study of engineering andCOVID-19 data. The statistical and mathematical properties of this distribution such as a linear representation ofthe probability density function, survival function, hazard rate function, moments, quantile function, order statistics,entropy, mean deviation, characteristic function and average residual life function are established. The estimates ofparameters of the proposed distribution are obtained using maximum likelihood estimation (MLE), Maximum productspacings (MPS), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. A Monte-Carlosimulation experiment is carried out to study the performance of MLEs. The applicability of the proposed distributionis evaluated using two real datasets related to engineering and COVID-19 death cases. All the computational workwas performed in R programming software.