In this paper, a new unit distribution is introduced. Some statistical properties of the proposed distribution are analyzed, including moments, Bonferroni and Lorenz curves, etc. Six estimation methods are investigated to estimate the three parameters of the proposed distribution. The performance of these estimators is compared using bias, mean square error, average absolute bias, and mean relative error using the Monte Carlo simulation. In addition, some real data analysis is performed using data sets on the amount of water from the California Shasta reservoir, the average failure times of a fleet of air conditioning systems, and skewed to-right data. A novel regression analysis is proposed based on the new distribution. A practical example illustrates its effectiveness and applicability compared to existing methods, including the beta, Kumaraswamy, and log-extended exponential geometric regression analyses.