Accurate estimation of compressibility factor is of great importance in predicting the performance of gas reservoirs using the material balance approach and also in the designing of gas pipelines and flowlines. Over the years, several correlations for estimating gas compressibility factor have been developed. However, these correlations have not been so successful in predicting the compressibility factor for High pressure-High temperature (HPHT) reservoirs and this explains why the industry still relies on the expensive and time-consuming constant volume depletion (CVD) approach. Therefore, this paper presents a correlation suitable for estimating the compressibility factor for high pressure-high temperature (HPHT) reservoirs using stochastic and robust optimization approach with Gaussian probability distribution. The results obtained shows that the correlation outperforms other pre-existing correlations within the range of pressures and temperatures considered.