The Continuous Bernoulli Distribution: Mathematical Characterization, Fractile Regression, Computational Simulations, and Applications

The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile position probability density function where corresponding surface fixed proportion. This article presents derivation of properties formulates or quantile regression model for response using exponentiated distribution. Monte Carlo simulation studies evaluate performance point estimators both model. Real-world datasets from science education are analyzed illustrate modeling abilities