Deterministic and accurate data analysis is the focus of classical statistics. However, in practice, there are a lot of instances where there is a degree of impreciseness, uncertainty, incompleteness, and vagueness in the information. In certain circumstances, traditional statistics may need to be more precise due to uncertainties. To increase data analysis accuracy in this situation, neutrosophic statistics are used. The Neutrosophic Transmuted Rayleigh (NTR) distribution is examined in this work. We present an extensive neutrosophic characterization of the NTR distribution statistical characteristics. The maximum likelihood estimation strategy, which is based on a neutrosophic environment, is used to estimate neutrosophic parameters. The performances of these neutrosophic estimators in terms of their neutrosophic biases and neutrosophic mean squared errors (MSEs) of the parameters have been compared using a Monte Carlo simulation research. Particularly helpful for modeling uncertain data is the generated distribution. Wastewater treatment data is used to demonstrate the utility of the NTR distribution for data modeling. Additionally, some recently proposed neutrosophic distributions are compared.