The gamma distribution is well-known for its wide range of applications across various fields. Traditional gamma distributions and their associated algorithms have been used to model imprecise data; however, they face limitations in addressing uncertainty and indeterminacy. To overcome these challenges, this study introduces the neutrosophic gamma distribution, an extension of the classical gamma distribution that incorporates neutrosophic random variables to better handle imprecision and indeterminacy. Basic properties of the neutrosophic gamma distribution are presented, along with algorithms designed to generate data under different levels of indeterminacy. Simulation results reveal that as the degree of indeterminacy increases, the corresponding random variates tend to exhibit an upward trend. Comparative analysis with classical statistics highlights the significant effect of indeterminacy on data generation. Overall, the study demonstrates that the degree of indeterminacy plays a crucial role in shaping the behavior of data derived from the gamma distribution.