The probability distribution is of great significance in probability theory, which is inherent in virtually all the branches of science. It is said to be used selectively in actuarial science with reference to insurance and finance, medicine, agriculture, demography and econometrics. However, the main contribution of the current research work is to propose a new distribution called as neutrosophic exponentiated power Lomax distribution or briefly NEPL. Several other mathematical characteristics that describe life survival and the related characteristics, such as hazard rate and functions and moment-generating functions and other tests of mean, variance, and standard deviation, asymmetry and kurtosis, have been built and analyzed. Monte Carlo method has been applied also to assess the efficiency of NEPL distribution estimate. Therefore, the results of the simulation carried out for this study reveal that the process of estimating with reasonable degree of accuracy is feasible only when the size of the sample is comparatively large. The existence of the premature infant staying time data has been utilised to illustrate the specific manner in which the elaborated NEPL distribution has been suggested for being applied. Based on the discussions of the previous sections, it can be deduced that the NEPL distribution is also general in terms of its applications because it can deal with all forms of data that is, it does not distinguish between certainty, probabilities of uncertainties, ambiguties or imprecisions.