In this article, a new bounded distribution on the unit interval (0, 1), namely, unit Mgamma (UMg), is presented. Different statistical properties, such as moments, median, mode, and hazard rate function are derived. Seven classical non-Bayesian methods are used to create a complete estimation framework. Monte Carlo simulation studies tells how well these estimators work by looking at bias, mean squared error, mean relative error, and other measures of discrepancy. The results consistently showed that the MLE method is better than the others, no matter what the sample size or parameter settings are. To demonstrate the practical utility of the proposed distribution, some real datasets constrained to the unit interval is examined. The model is compared to several well-known distributions that compete with it, such as the beta, Kumaraswamy, unit Lindley, Johnson $S_B$ and unit Gompertz distributions. We useed goodness-of-fit measures like log-likelihood, the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and Kolmogorov–Smirnov (KS) statistics to make the comparison. The results showed that the proposed model fits the data better, both in numbers and in graphs. These findings highlighted the flexibility and effectiveness of the proposed unit Mgamma distribution as a competitive alternative for modeling bounded data.