This study introduces a new flexible bounded model on the unit-interval (0,1) obtained through a nonlinear transformation of the Weibull distribution called the Nagarjuna distribution. The flexibility of the proposed distribution allows it to accommodate different shapes, including symmetric, skewed, U-shaped, decreasing density forms and other new types forms, along with various risk function behaviors, such as increasing, decreasing and bathtub shapes. Several important properties of the distribution have been studied, including its moments, moment-generating function, and order statistics. The distribution parameters were estimated using the maximum likelihood estimation, maximum product spacing, and least squares methods, and their performance was extensively examined through simulation studies. Actuarial risk measures are considered to highlight the distribution’s ability to handle different levels of risk. Finally, the practical usefulness of the proposed model is demonstrated using real data, showing that it provides an effective tool for modelling bounded data.