A continuous probability distribution on the unit interval (0,1) constructed as the ratio W = X1/(X1 + X2) of two correlated Frechet random variables from a bivariate extreme-value distribution with Frechet margins. Students learn how the model's cumulative distribution and density are derived, and how its properties are established: identifiability, symmetry, a stochastic representation, its characterization as a ratio, moments, stress-strength probability, quantiles, and maximum likelihood estimation validated by Monte Carlo simulation. The construction generalizes the classical independent-Frechet ratio model by allowing dependence between the two margins, giving a flexible model for bounded (0,1)-valued data.
A methodological statistics paper proposing a new continuous probability distribution supported on the unit interval (0,1), obtained as the ratio W = X1/(X1 + X2) where (X1, X2) are two correlated Fr…