A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications

This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, U, hazard rates. model define well-known distributions with various parameters supports, such as Kumaraswamy, exponential, exponentiated uniform, generalized of first kind, power distributions. We present comprehensive account mathematical features model. Maximum likelihood methods Bayesian method under squared error linear exponential loss functions are presented; also, approximate confidence intervals obtained. simulation to compare all results. Two real-world data sets analyzed demonstrate utility adaptability proposed